inescc.pt - Lamsade - Université Paris
Contents
1. P P P s S s s s s S s s S s s S S s c a a a a a a a a a a a a a a a neee WO POH 01000 HR Jo R PWOOrRFOAWARNUB WN JO RRRPHAS0O00 Rs NO TWA AW O Nob BBB A A BW A ASAS IRIS 2 0 User Manual 38 16 9 12 4 Saul 4 9 DAS 2253 29 5 8 6 29 64 5 bounds on 49 49 49 49 49 bounds on weights 01 01 01 0 01 ional constraints O 1 0 0 0 on lambda a a a a a o K K K K K o K K K K K e K K K K K e O OnE n BWQQQUOQ BZFPHHHHHHPNNNNWN w MOQO O D m 0 name of criteria END OF FILI IRIS 2 0 User Manual 39 Appendix B Importing data from MS Excel Sometimes the user may already have data in a spreadsheet like MS Excel namely a table that indicates the performances of the actions at the several criteria This appendix shows how these data may be easily imported into IRIS For instance let us assume that the performance data of 10 actions at 5 criteria were in a file example xls as follows if the actions were in columns instead of rows we could use the TRANSPOSE function in Excel Y example xls AAA A ASA pa Pertormancedata O 2 action ot 00 so so so 3 las 7 wm s _ p oa a a 4 5586 97 ise To import these data the user may proceed as follows 1 Start IRIS 2 Create a new file indicating 10 actions 5 criteria and th2. considering all the criteria e Ais the cutting level For each criterion 1 n a concordance index indicates how much that criterion agrees with the hypothesis a S bx which is computed as follows IRIS 2 0 User Manual 8 4jbn 4 Pj On Aj Pj On 4j bn if pj On S Aj lt aj bn 1 if A gt g j dp The concordance is maximum 1 when a is better than b or is worse but by a small difference up to g b When a is worse than b the concordance starts to decrease when the difference in favor of b becomes larger than q b and attains its minimum 0 when the difference in favor of bp becomes equal to or greater than p b c a by P Dp qj Dp 0 A The n single criterion concordance indices one for each criterion are then aggregated into a global multicriteria concordance index considering the relative weight k of each criterion c a by Xi kjcj ai bn where we assume that TL de j On the other hand for each criterion j 1 7 a discordance index indicates how much that criterion disagrees with the hypothesis a S bx which is computed as follows 1 if Aj lt v by d aby 4 Aj ujlbn v bn u bp if v by SA lt u bp 0 if A gt u dp The discordance is minimum 0 when a is better than b or is worse but by a difference up to u b where u b 2p b When a is worse than b the disc
3. 1 Ak Kn 20 Y Y 0 1 This mathematical program is equal to the former except the introduction of a new constraint Lie s Vi lt S 1 This constraint prohibits the former optimal solution or a superset of that solution e A set Sis formed from the new optimal solution as explained for the case of S e Set p lt 3 add the constraint Lies y S S2 1 etc e The process stops as soon as a pre defined number of sets is reached or when the 0 1 programming problem becomes infeasible which means that there are no more alternative ways to restore the consistency of 1 8 IRIS 2 0 User Manual 16 4 Software presentation 4 1 General structure IRIS is a SDI Single Document Interface program like for instance Microsoft Explorer This means that the user can work at a single document problem at a time Of course the user can work on several problems at the same time by running several instances of IRIS simultaneously The program runs on a single window and the user can change its position change its size minimize it etc This window is divided in two areas The left area of the screen is for inputs whereas the right area of the screen is for outputs Each area is organized according to a multi page notebook metaphor with tabs to change pages The space occupied by each area may be changed by clicking on the dividing line and dragging it to the left or to the right When inputs change outputs
4. 1 p or ISI 2 15 Each one of the sets S S2 S presents an alternative manner to restore the consistency The end user should choose one of these sets which are presented by increasing order of cardinality and remove or at least relax the constraints in that set The interaction may then continue as explained in the previous section The method to compute these sets is the following one e Set pel e Solve the 0 1 programming problem min VJ ZX Akp kn M y1 y 20 ki kz k 1 A kr Kn gt 0 Y Vz 0 1 IRIS 2 0 User Manual 15 In this mathematical program M denotes a very large number and z denotes the number of constraints in the system 1 7 Each of these constraints is associated with a variable that can take only the values 0 or 1 Since these variables are multiplied by an arbitrarily large number setting any of these to the value 1 amounts to ignore the corresponding original constraint The objective is to minimize the sum of these variables so that all would be zero if the system 1 8 was consistent e Since the system 1 8 is not consistent the optimal solution to the above problem will contain several y 1 ie 1 z Let S f ie f1 z y 1 Then removing the constraints indexed by S from 1 8 would result in a consistent system e Set p2 e Solve the 0 1 programming problem min Y Yi ZX Mkp kn M yp y 0 gt 0 Ki tkot k 1 Dies Yi HS
5. 28k 1 4 c 31p 2 Is c 31k 4 e Jai z Jaz a fad3 a Jaa 110 fas LB lambda 1 4 Max suggestions 5 IRIS 2 0 User Manual 27 5 A step by step example 5 1 Opening a project To open a file created previously the user run IRIS choosing one of the two versions available either irisl exe or irislsi exe The latter version does not include the inconsistency analysis module but does not require to have LINGO previously installed From the menu File the user must then choose the option Open and locate the file which usually will have a tri extension Alternatively to using the menu the user may click on the button A E 3 Floppy 4 TA a C 28 Audio CD D To follow this example the user should locate the file testl tri which comes with IRIS The path and name of the file will appear in the caption of the IRIS window IRIS 2 0 C My Documents test1_tri IRIS 2 0 User Manual 28 5 2 Obtaining results After opening a project using FilelOpen or a or after creating a new one using FilelNew the user may start editing the file and obtaining results Choosing ResultslVolume Computation allows to compute the relative volume of parameter polyhedron that respects the constraints imposed so far i e the constraints which state that kz is not lower than any other k 2 according to the data in the Constr
6. A E File Categories Criteria Actions Constraints Results Inconsistency Help CELLS Heigthfi6 Wwidthf2e Font size je The Results page uses color to indicate the range of possible assignments for each action robustness analysis i e the categories where it may be assigned without violating the constraints bounds and assignment examples These ranges appear in green color In some situations there are some intermediate categories where an action cannot be assigned recall Section 3 4 1 as for instance a28 in the figure above when a28 is good enough to be better than C then it reaches C3 without being assigned to C2 These situations are presented to the user as a hole in a range In each range one of the cells has a darker shade of green meaning it is the assignment recommended by IRIS based on the inferred combination of parameter values This combination is chosen to be relatively central to the set of combinations that respect all the bounds constraints and examples It is presented in the last row of the Results page in green color If the user selects any cell in a range then the penultimate line in the Results page shows a combination of parameter IRIS 2 0 User Manual 24 values that assigns the action in the cell s row to the category in the cell s column For instance the figure above shows a combination of values that assigns a28 to C5 The actions that are assignment examples can easily be identified by the b
7. However the most important outcome may be that the end users will increase the insight on their view of the problem learn about their preferences and will possibly modify their opinions IRIS 2 0 User Manual 14 3 6 Dealing with inconsistencies It may occur that after introducing some constraints the system of inequalities 1 k 2 LB 1 n 2 k 2 UB j 1 n 3 A 2 Amin 4 A gt Anas 65 ciai De yla HL ki 2 45 BC yla m1 k2ttcn aibe yta 1 Kn ZME as by aie A 6 c a bC a k 0 gt a ba ta k gt ld Poda Aa aje A 7 Qo A Op ki Onz Kn 2 B 2 1 Mcons Sk k Kk 1 becomes inconsistent i e there does not exist any combination of values for the parameters Ak k able to satisfy all the constraints simultaneously Besides the information referred to in the previous section there are methods to compute alternative ways of restoring the consistency by removing some constraints Mousseau et al 2003 One of these methods uses mixed integer programming continuous and 0 1 variables to compute a succession of sets of constraints Sy So S Such that 1 Vie f1 p if the constraints in S are removed from system 1 8 then it becomes consistent 2 VieEfl p Hj Si S 3 Vie 1 p i lt j 151 SISA 4 If removing a set of constraints S from the system 1 8 makes it become consistent then either S S i
8. The Inconsistency option becomes available on the main menu leading to a window where the user learns some suggestions on how to overcome the inconsistency for details refer to Section 4 5 In that window which may be moved and resized independently from the main window the user just has to indicate the maximum number of suggestions and press the button Suggest In this case there exist two possible ways to restore the consistency either to remove constraint 2 i e that as belongs to category C or lower or to remove constraints 1 i e that az belongs to category C4 and 8 i e that the cutting level cannot exceed 0 99 Closing this window returns the user to the main IRIS window Information x G There are no more alternatives la UB lambda lg fek Max suggestions Js Help IRIS 2 0 User Manual 32 5 6 Producing a report The user may choose FilelReport after having computed any results If issued at this point in the example the report coincide with example 2 in Appendix C The user may select the name and location of the report file 5 7 Further interactions At this point recall section 5 5 since constraint 8 cannot be relaxed the user would remove constraint 1 To perform this in the Actions page set the EHigh column cell corresponding to a to the value of 4 Recomputing the results we are back to the previous situation presented below with the results sorted by variability order Ac
9. accompanying written materials including this report Technical support INESC Coimbra may provide technical support via e mail ecretaria inescc pt and entitles you to receive news and information regarding the purchased software ORDERS Copies of this report may be ordered to Instituto de Engenharia de Sistemas e Computadores de Coimbra Rua Antero de Quental 199 3000 033 Coimbra Portugal Tel 239851040 Fax 239824692 IRIS IRIS Interactive Robustness analysis and parameters Inference for multicriteria Sorting problems Version 2 0 User Manual Luis DIAS Vincent MOUSSEAU Coimbra INESC Coimbra 2002 45p Documentos do INESC Coimbra ISSN 1645 4847 IRIS Interactive Robustness analysis and parameters Inference for multicriteria Sorting problems Version 2 0 User Manual Lu s DIAS and Vincent MOUSSEAU 1 INESC Coimbra 3 LAMSADE Universit Paris Dauphine Rua Antero de Quental 199 Place du Mar chal De Lattre de Tassigny 3000 033 Coimbra PORTUGAL 75775 Paris Cedex 16 FRANCE 2 Faculdade de Economia Universidade de Coimbra Av Dias da Silva 165 3004 512 Coimbra PORTUGAL Abstract This document is the User Manual for the decision support software IRIS Interactive Robustness analysis and parameters Inference for multicriteria Sorting problems Version 2 This tool has been built to support the assignment of actions alternatives projects candidates described by their evaluatio
10. become invalid which is shown by using a red font in the output pages The outputs will reflect the changes in input only after the option Robust Assignments from the Results menu is chosen or as a shortcut press Alt R then R IRIS 2 0 C My DocumentsiCahier2 tri File Categories Criteria Actions Constraints Results Inconsistency Help CELLS Heigthfi6 Width 23 Font size le y Results Infer Prog Indices fer fea fc cs fc5 22 OS 0 0 017 0 315 0 307 0 3076 0 017 0 01 76 0 017 0 71620 12620 24250 12620 12620 12620 12620 1262 There are some grids associated with input and output pages The user can edit the height width and font size of the grid elements by setting their values at the right top of the screen Heights Wiath 52 Fontsiefe It may happen that the contents of some grid cells cannot be displayed in its entirety In such cases if the user does not wish to enlarge the width of the cells he she may position the mouse over the cell so that its contents will be entirely displayed All of the input or output pages have pull down IRIS 2 0 User Manual 17 menus associated with them To access these menus the user just has to click on the right button of the mouse or select the pull down menu key that is available in some keyboards The last option in each menu Help leads directly to the page of the on line manual related to the current page 4 2 Input The inputs must be read f
11. criteria and actions menus described just above and an option for getting specific help e Fixed Par page A menu gives access to the options in the criteria and categories menus described just above and an option for getting specific help e Bounds page A menu gives access an option for getting specific help e Constraints page A menu gives access to the options in the constraints menu described just above and an option for getting specific help e Results and Infer Prog pages A menu gives access an option for getting specific help
12. examples where the users indicate minimum and maximum categories for some of the actions according to their holistic judgment These assignment examples are translated into constraints on the parameter values meaning that the assignments of ELECTRE TRI should restore these examples e When the constraints are inconsistent IRIS infers a combination of parameter values that least violates the constraints by minimizing the maximum deviation Furthermore a module becomes available to determine the alternative subsets of constraints that must be removed to restore the consistency e When the constraints are consistent IRIS infers a central combination of parameter values by minimizing the maximum slack For each action it depicts the category corresponding to that combination as well as the range of categories where the action might be assigned without violating any constraint robustness analysis For each category in the range IRIS may also determine a combination of parameter values that assigns the action to that category e Moreover when the constraints are consistent IRIS may compute some indicators concerning the precision of the inputs by estimating the volume of the polyhedron of all feasible combinations of parameter values and the precision of the outputs by indicating the geometric mean of the number of possible assignments per action IRIS 2 0 User Manual 5 2 1 What is new in IRIS 2 IRIS 2 0 has benefited from imp
13. interactions meta cialis 32 328 Creating a New project iii A a sa daa 33 Credit a A Ei 34 A A A eeu sien g alee tance a NT e TA 34 Appendix A Syntax of the input file tri oe eee csecseecscecnseceseceseceseceseceeesseesseeseneeeaeesaeeenaeenaes 35 Appendix B Importing data from MS EXCel uo cece eesceeseeessecssecesecnseceaeceseceeeeseeeeeeeeeeseaeesseeeaaeenaes 39 Appendix C Syntax of the report file rpt oo eee eeeeseeseecnseceseceseceseceseceseesseessneseneseaeeeaeeeneeenaes 41 Appendix D Men StrUctUrE crias ie lidia selgectesdelecetscceett tactey 44 IRIS 2 0 User Manual 3 1 Getting started Obtaining the IRIS Software IRIS runs on Windows 95 98 Me XP computers The monitor should be at least VGA 640x480 with 16 colors It occupies little space on disk and is not too demanding in terms of RAM however the more the better The program may run without a mouse but becomes somewhat cumbersome to use You should have a 2 button mouse to make the best use of this software To install IRIS unzip the contents of the file iris2 zip to a new folder with a location and a name of your choice IRIS may be purchased form INESC Coimbra a non profit Portuguese R amp D institute owned by the University of Coimbra and INESC INESC Coimbra Fax 351 239 824692 Rua Antero de Quental 199 Phone 351 239 851040 3000 033 Coimbra Portugal C O Luis M C Dias LDias inescc pt IRIS page in the Internet www4 fe uc pt Imcdi
14. the inputs e The by Input Order option instructs IRIS to sort the actions by their input number e The by Variability Order option instructs IRIS to sort the actions by decreasing variability order where variability refers to the difference between the best and worst possible assignments The outputs area of the screen updated after choosing the option Robust Assignments may be enlarged or reduced and contains the following pages 4 3 1 RESULTS PAGE This page displays a grid with the inferred parameter values and assignments as well as the range of possible assignments for each action Depending on the selection previously made in that menu by Input Order or by Variability Order the actions appear in the same order as the Actions page e g first figure below or appear by decreasing order of variability e g second figure below where variability here means the difference between the best and worst categories in the actions assignment range The user may change the actions order at any time even after the results are computed IRIS 2 0 User Manual 23 IRIS 2 0 C My DocumentsiCahier2 tri OF ES File Categories Criteria Actions Constraints Results Inconsistency Help CELLS Heigth 16 Width 28 Fontsize e Results Infer Prog Indices fer fc fc cs fes o E 0 0355 0 2426 0 035 0 217 0 217 0 217 0 035 0 71620 12620 24250 12620 12620 12620 12620 1262 IRIS 2 0 C My DocumentsiCahier2 tri
15. this lower bound should not be lower than 0 5 4 A 2 Amar note this upper bound should be lower than 5 ciai De yla HI KI 2 45 BC yla m1 k2 Cn ai gt Dc a 1 Kn ZME as by aic A 6 cy a Bc a k1 2 41 PGyeg a 3 k2 gt Cp 85 gt bc a kn Z A Bid a i A T Qo A Oly ki One Kn 2 Bo 2 1 Mecons to which we add Sk k Kk 1 Let us write 1 7 in a more compact matrix notation as Z xX Ak kn gt 0 where Z is an appropriate matrix with as many rows as the number of inequalities in 1 7 and n 1 columns Now the following linear program may be used to infer the parameter values 1f exist that satisfy all the constraints which implies restoring all the assignment examples with greatest slack min ae R A ZX Ak k O k k 1 the variables are 0L A k Kn If the minimum its optimal value is zero or less then the system Z X Ak K J gt 0 is consistent and the optimal value for the variables A k k satisfies all the constraints Otherwise if the minimum Q is positive then there does not exist any combination of parameter values able to satisfy all the constraints in 1 8 simultaneously see Section 3 6 on dealing with an inconsistent system of constraints 3 4 Robust assignment ranges Let us consider again the system ZxX Mk ka 20 k k 1 introduced in the previous section which represents all t
16. values must be explicitly inserted as a number a blank cell originates an error 4 2 4 CONSTRAINTS PAGE When working in the Constraints page the user may edit the constraints other than bounds and assignment examples that the weights and cutting level should respect The constraints may be directly input in the corresponding cells The first normalization equality yellow color is fixed The user may navigate between the remaining cells using the mouse or the keyboard arrow keys Zero valued coefficients may be left blank indeed to improve readability IRIS hides all the zero values except those in the RHS column The right hand sides cannot be negative but the remaining coefficients can To enter the type of inequality type lt or just lt which is considered the same or gt or just gt The user may change the number of constraints either creating new ones or deleting some of them The constraints menu and the corresponding pop up menu offer the commands to perform this The option of deleting asks the user which constraint is to be deleted and the constraints identification labels change accordingly after the deletion File Categories Criteria Actions Constraints Results Inconsistency Help ele CELLS Heigthfi6 width 28 Font size a Results Interred cons 4 In the above example the constraints ad to ad6 force k to have a value which is not less than any of the other weights
17. vee trad a dd onions aS 10 3 4 1 Impossible assignments Within a range ee eee eseesecseeceseceseceseceseeeseeeseeeeeeeeneeeaeeeaaeenaes 11 3 5 Interaction process to build an ELECTRE TRI model ooooonnconnccnocononcconnnonnconnnnononaccnnncrancnnnnos 12 3 6 Dealing with Inconsistencies siniori t e IA ade 14 A SoftWare presentation oscars dais T 16 4 1 General structure ini aii italia 16 4 2 NN 17 ADV Actions PAL ai a gis 17 42 2 Fixed parameters page oriori i o terse tang feces a aha ete peatee es beat aa 19 4 2 3 Bounds Pale nitratos 20 4 24 Constraints Paleo lr ita ii data 21 43 QUtPUt nan onian e a iets Ane ee Mets ene a ee tae lates 22 AS TEIROSUIES DARE ciate cece tose le aan coin naa Dn E ni 22 4 3 2 Inferred constraints page 0 0 ccceeccesessceeeceseceeeeeesececeeseeseceaecaeeeeesecseeeceesecaeeaeeeeeeaeeas 24 4 3 3 Infer PROG Page cin ede EEEE E E E TEE EES 25 4 34 Indices pagenan nnn e A AA 25 AA Results Tepon era sateen eee a oan aa r ee raceme vets Reed e er aaaea aE nE PERAE Ea 25 4 5 Inconsistency analysis srono ei aaa aes n seede tiana diia ee ede 26 SAALSEP DysSlEP CX AMP AAA OR ORO 27 IL Opening A projectie riie A E se en ea e E ata 27 D2 SOD TAMING results inuit a e A E E AE EEA RE E A O A 28 3 Editmg TASINPU S Mia EE E E E e E E E Ee A ES e EEE 29 SA NS NO 30 5 52 Obtain new results nnee A ee EE E 30 ds A alyzime MCONSISTENCIES ii A a Ue 30 5 6 Producing a TE POM tt didnt int did 32 Te Further
18. worst category W a the inferred category a and the best category B a for each action a These are separated by the tab character When the inputs are inconsistent the worst category and the best category are blank RESULTS ACTION Worst Cat Inferred Cat Best Cat name W a 1 a B a The third part of the report presents the constraints to the inference mathematical program that minimizes amp The last column Error appears only when the system of constraints is inconsistent indicating by how much is the constraint violated 1f Error is positive or the existing slacks 1f Error 1s negative Let us denote each constraint as following the pattern Bj BoA Bakit B nkr S 2 n3 INFERENCE PROGRAM Descr alpha lambda kl Pe kn lt gt RHS Error label B B2 Bo Bas lt gt Bm3 error The last part of the report presents the optimal solution ho ki way Kk A to the inference program INFERRED SOLUTION lambda k1 oy kn a ki k The format of this results file makes it convenient to be read by a text processor or a spreadsheet IRIS 2 0 User Manual 42 Example 1 consistent system INPUT FILE C My Documents testl tri RESULTS ACTION Worst Cat Inferred Cat Best Cat 4 WN Ud Y WU WM UY AB BWW WB Y 4 3 4 3 3 3 3 4 3 3 3 3 3 3 2 3 Y 3 3 1 N Ud W ROUND 000 Ud ds ds ds 0 de ds QU gt INFERENCE PROGRAM Descr alpha lambda C 2 gt 4 1 il c 28 lt
19. 1 1 adl Jl ad2 T ad3 al ad4 dl LB lambda 1 dl dl 1 1 x m gt MS al A Vv ve a un V ll o hb he hb bh UB lambda k1 k1 k2 k2 k3 k3 k4 k4 k5 al k5 1 E C E C E C E 1 C ln w w u www w w wW w EEN oo ODIO OOO NODOS OTO D ODTOD ODRA ROTO O OOOO OGOO RAH OOOO Or OOO OOA A OO Or OF ie Ree ooocorRrFOCOAOCOCOCO OO oorroo00o0000o0o0ol l oo o0o000000000000000o0Oo SS O s Odds Odds Odds O 0 OFMOFWOFWOFWOF U INFERRED SOLUTION lambda k1 k2 k3 k4 k5 0 80004 0 10498 0 39002 0 10498 0 10498 0 29504 IRIS 2 0 User Manual 43 Example 2 inconsistent system INPUT FILE C My Documents testl tri RESULTS ACTION Worst Cat Inferred Cat Best Cat 4 3 2 2 3 3 3 3 3 2 3 2 3 3 2 3 INFERENCE PROGRAM Descr alpha C 2 gt 4 1 C 5 lt 2 al adl 1 ad2 T ad3 1 ad4 dle LB lambda 1 al 1 1 1 x ws x ul jan n Error 0 00505 0001 0 00505 0 32003 0 31498 0 00505 0 00505 0 39505 0 00505 505 48505 31498 16502 hb hb m bh hb Pe Eb hb UB lambda k 1 k 1 k2 k2 k3 k3 k4 k4 k5 al k5 1 No E E Cc vo H C E O H 48 3200 215997 32003 15997 C E O H 1 C E Y w ww w w OGOGO GOO OGO OGOOGO OOOO O o0000000000rroooot o0o00000000o0rro0ooool 000000
20. ISSN 1645 4847 Instituto de Engenharia de Sistemas e Computadores Institute of Systems Engineering and Computers INESC Coimbra Da IRIS Interactive Robustness analysis and parameters Inference for multicriteria Sorting problems Version 2 0 User Manual Lu s DIAS and Vincent MOUSSEAU Documents of INESC Coimbra No 1 2003 April 2003 INESC Coimbra LIMITED WARRANTY AND DISCLAIMERS Limited warranty on media INESC Coimbra warrants the disks on which the software is recorded to be free from defects under normal use for a period of 90 days from the date of delivery INESC Coimbra will replace the disk at no price to you provided you return the faulty disk to INESC Coimbra Disclaimer The software is provided as is without any warranty of any kind including but not limited to the implied guarantees of merchantability and fitness for a particular purpose INESC Coimbra does not warrant guarantee or make any representations regarding the use or the results of the use of the software or any accompanying written materials in terms of their correctness accuracy reliability currentness or otherwise In no event will INESC Coimbra or its researchers employees directors or affiliates be liable to you for any consequential incidental or indirect damages including damages for loss of business profits business interruption loss of business information and the like arising out of the use or inability to use the software or
21. The ELECTRE family of methods has been created in the 1960 s by Bernard Roy and his collaborators e g see Roy 1991 Roy and Bouyssou 1993 It consists of several methods developed for the choice and ranking problematics and a method to deal with the ordinal sorting problematic the ELECTRE TRI Yu 1992 Roy and Bouyssou 1993 Let us introduce some notation e m number of actions e n number of criteria e t number of categories e A fa Gn set of actions e G fgui Zn set of criteria real valued functions on A e C f C Cj set of ordered categories C is the worst one C is the best one e Bz bp bi set of profiles reference actions that separate consecutive categories IRIS 2 0 User Manual 7 Each category C is limited by two reference actions profiles b is its upper limit and b is its lower limit Criterion 1 Criterion 2 Criterion 3 Criterion n The assignment of actions to categories is based on the concept of outranking relation on AXB An action a A outranks a profile b e B denoted a S bn if it can be considered at least as good as the latter i e a is not worse than b given the evaluations performances of a and b at the n criteria If a not worse than b in every criterion then it is obvious that a S b However if there are some criteria where a is worse than b then a may outrank b or not depending on the relative importance of
22. a A JAB BA FR A 18 gt Y Using the mouse the user may select the remaining pages and change the values corresponding to the fixed parameters Section 4 2 2 Fixed Par page the bounds on the criteria weights and the cutting level Section 4 2 3 Bounds page and the constraints on those parameters Section 4 2 4 Constraints page The outputs page becomes invalid after inputs are IRIS 2 0 User Manual 30 changed which is shown by the use of a red font Results must be re computed to reflect the changes in the inputs An alternative to editing the inputs using IRIS is to edit the inputs file using a text processor or a spreadsheet saving the file in text format The syntax of the inputs file usually with a tri extension is described and exemplified in Appendix A 5 4 Saving the data To save the data the user may choose between the options FilelSave Data and FilelSave Data As The button H corresponds to the latter option which asks for the file s name and location and allows to save it under a different name e g test2 IRIS automatically appends the extension tri The caption of the IRIS window will reflect the change 5 5 Obtaining new results The red font in the outputs page shows that the inputs have changed To reflect these changes in the results the user must re calculate the results by choosing ResultsIRobust Assignments The assignment example that az belongs to Cy causes a re
23. aints page plus the bounds imposed in the Bounds page The user may choose a precision which is three digits by default press the button Start simulation and wait for the simulation to end IRIS Volume Computation 0 x n zi Precision E Se Dimension 5 Absolute Volume 0 00186 Volume to bounds 0 201 Exit In this example the 6 dimension polyhedron of acceptable values for the weights and cutting level has a dimension of 0 00186 Considering only the combinations that respect the bounds defined in the Bounds page about 20 of them respect the constraints in the Constraints page The user may now press the Exit button to return to the main window Choosing the option ResultsIRobust Assignments IRIS will determine the range of categories where each category may be assigned to given the polyhedron of acceptable values for the parameters indicating the inferred central parameter values as well as the precise assignments corresponding to these In this example the user may notice that action az cannot be assigned to category C3 Recall Section 4 3 to know how to interpret these results and interactively calculate some other ones For instance action az was assigned to C3 but might also have been assigned to C3 or C4 without violating any constraint Selecting any of these cells will instruct IRIS to calculate a combination of parameter values leading to the selected assignment The user may select the order of pr
24. as iris htm IRIS 2 0 User Manual 4 2 A brief overview of IRIS IRIS is a Decision Support Software designed to address the problem of assigning a set of actions to predefined ordered categories according to their evaluations performances at multiple criteria For instance it may be used to sort funding requests according to merit categories e g Very good Good Fair Not eligible or to sort loan applicants into categories e g Accept Require more collateral Reject or to sort employees in a company into categories that define incentive packages etc IRIS implements a methodology developed by Luis Dias Vincent Mousseau Jos Figueira and Joao Climaco presented in Dias et al 2002 see also Section 3 which is based on the ELECTRE TRI method see Roy and Bouyssou 1993 and Yu 1992 The inconsistency analysis method is presented in Mousseau et al 2003 see also Section 3 The main characteristics or IRIS are e IRIS implements the pessimistic ELECTRE TRI using a variant of the original function to compute discordance veto effects as proposed by Mousseau and Dias 2002 e IRIS accepts imprecision concerning the criteria weights and the cutting level The users may indicate intervals for each of these parameters as well as linear constraints on the weights Furthermore the constraints may be defined indirectly as indicated in the next item e IRIS accepts assignment
25. criterion The user may also disable enable veto for all the criteria by selecting unselecting the button Use vj figure below on the left When Use vj is not selected IRIS considers s a b c aj Dp The user may choose to work with discordance thresholds also instead of letting them take the default value u b 0 25 pf b 0 75 v b To enable disable the use of explicit discordance thresholds the user may select unselect the button Use uj figure below on the right This button is available only when the button Use vj is selected As for the veto thresholds discordance thresholds with value 0 are ignored and hidden IRIS 2 0 User Manual 20 Actions Fixed Par Bounds Constraints Actions Fixed Par Bounds Constraints 600 300 1000 300 600 300 1000 300 600 300 1000 300 ut vi afb 2 p2_ uz alba 3 p3 ua 3 afb E ps 600 300 1000 300 E El Use vj Use uj Use vj Useui The last row in the grid indicates if the preference increases or decreases with the performances If the value is then the higher the performance the better the criteria is one to be maximized such as customer satisfaction If the value is then the lower the performance the better the criteria is one to be minimized such as fuel consumption The user may navigate between cells using the mouse or the keyboard arrow keys All inp
26. d criteria names will be lost v A progress bar appears when results are being computed which can be noticed in problems of large size IRIS 2 0 User Manual 6 3 Methodology 3 1 The sorting problematic Roy 1985 defines four problematics types of problems in multicriteria decision aid e description problematic the purpose of the analysis is to describe the decision situation in a formal language in terms of actions criteria and evaluations e choice problematic the purpose of the analysis is to select one action or a limited number of actions e ranking problematic the purpose of the analysis is to rank the actions by order of preference e sorting problematic the purpose of the analysis is to sort the actions into categories defined a priori The sorting problematic evaluates each action according to its intrinsic absolute merit Each action is assigned to a category independently from the remaining actions If the categories are ordered according to the Decision Maker s preferences e g the categories high risk medium risk low risk very low risk in the evaluation of applications for credit the problematic may be called ordinal sorting Otherwise the problematic may be called nominal sorting e g separating job applicants according to the categories creative profile technical profile human relations profile leadership profile 3 2 ELECTRE TRI
27. d the cutting level combining parameter inference Section 3 3 and robustness analysis Section 3 4 At a given iteration the input may consist of a system of constraints 1 8 on the criteria weights and the cutting level recall Section 3 3 besides fixed values for the actions perform ances the profiles and the indifference preference discordance and veto thresholds The general idea is to start with few constraints of the parameter values adding more inequalities as a product of an interactive learning process about the problem and the method For instance the user may start with loose bounds for the criteria weights e g 0 1 lt k lt 0 49 and the cutting level e g 0 51 lt AS0 99 and no further constraints or assignment examples In any iteration the system of constraints corresponding to the input information may be consistent or not The analyses that may be performed will depend on the presence or absence of a consistent system If the system is consistent In this case there will be a set of combinations of values for the variables A k k that satisfy the system 1 8 i e restore all the assignment examples and simultaneously conform to the additional constraints The interaction should aim at reducing the set of accepted combinations of parameter values either by modifying a constraint or adding a new one To guide the user in this task several results may be computed e a central combination of pa
28. duction of the set of acceptable values for the parameters and hence leads to decrease in the ranges of possible assignments This is visible in the Results page An indicator for the reduction the geometric mean of the number of categories in a range is presented in the Indices page Results Inferred constraints Infer Pro 4 gt Results Inferred constraints Infer Prog Indices GEOMETRIC MEAN FOR No CATEGORIES Including examples 1 347 variation 0 241 15 2 0 73 0 22 O36 014 O14 O14 5 5 Analyzing inconsistencies The results now show that action as can be assigned either to C or C the inferred suggestion Let us suppose however that according to the user s experience that action should be assigned to C3 at the best Obviously that is inconsistent with the constraints imposed so far as IRIS will state when IRIS 2 0 User Manual 31 the user introduces this example via the Actions page as exemplified above and re calculates the results ResultsIRobust Assignments The assignments corresponding to the new inferred parameter values are presented in red color in the cases where the examples have not been restored a and as IRIS 2 0 C My Documentsttestl tri Al ES File Categories Criteria Actions Constraints Results Inconsistency Help 3 CELLS Heigthfie Width faz Font size le Results Inferred constraints Infer Prog 0 9950 0 0049 0 3249 0 01 0 330070 3300
29. e number of categories Section 5 7 3 Save the file choosing its location and name e g example tri Section 5 4 4 In Excel open the file example tri accepting the default choices proposed by the Text Import Wizard Original Data Type Delimited Delimiters Tab Column Data Format General IRIS 2 0 User Manual El Microsoft Excel example tri Dee Edit View Insert Format Tools Data Window Help 0 0 0 0 0 0 0 0 0 0 9 c Thresholds 1 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 1 0 0 0 0 2 0 0 0 0 2 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 20 c Actions 0 0 0 0 0 1 3 0 0 0 0 0 0 1 3 1 0 0 0 0 0 1 3 2 0 0 0 0 0 1 3 3 0 0 0 0 0 1 3 4 0 0 0 0 0 1 3 5 0 0 0 0 0 1 3 6 0 0 0 0 0 1 3 E 0 0 0 0 0 1 3 8 0 0 0 0 0 1 3 9 31 c Upper bounds on weights 5 Copy the data in cells B3 F12 from example xls to the cells B21 F30 in the file example tri 6 Save example tri keeping the text tab delimited format and close that file 7 Re open example tri in IRIS it now contains the copied data 40 IRIS 2 0 User Manual 41 Appendix C Syntax of the report file rpt The first part of the results report indicates the name of the input file used to derive results This gives the user the possibility of saving the inputs under a convenient name before producing the results report so that the two files are congruent INPUT FILE Full path of the file The second part of the report indicates the
30. econd best category from the best one Each line will present a profile that dominates the profile presented in the preceding line If we denote by g b the performance of the r profile according to the j criterion then the successive lines should appear as follows the id_number is ignored but must be present p id_number g b 8 b 8n 1 p id_number g b2 gabo gn b2 pP id_number 81 D 1 8b 1 En D 1 e Afterwards IRIS expects n t lines starting with an s to present the thresholds associated with the criteria profiles In each line the first number after s identifies the profile an integer between and t the second number identifies the criterion an integer between and n the IRIS 2 0 User Manual 36 third number indicates the indifference threshold the fourth indicates the preference threshold the fifth indicates the discordance threshold 0 if disabled and the last indicates the veto threshold 0 if disabled If we denote by g b p b ujb and v b respectively the indifference preference discordance and veto thresholds associated to the j criterion given the performance of the r profile then the successive lines should appear as follows r 1 t 1 j 1 n s r jo qb p b ufb v b e Next IRIS expects m lines starting with an a to present the performances of the actions and possibly assignment examples In each line a first number after a an int
31. eger identifies the position of the action followed by n numbers indicating the performances of the action at the multiple criteria Then there should appear two integer numbers between and 1 the first one constraining the action s assignment from below i e indicating its worst envisaged category and the second one constraining the action s assignment from above i e indicating its best envisaged category If the first of these two numbers is higher than or if the second of these numbers is lower than f then these actions will belong to the set of assignment examples Finally all the characters until the end of the line will beco me the action s name If we denote by gj a the performance action a at the j criterion by Cwors ai its worst envisaged category and by Cyes a its best envisaged category then there should appear m lines as follows a i 81 ai go a e gn a Cworse Gi Chest Gi name e The next block IRIS looks for presents the bounds for the criteria weights one line per bound Each of these 2 n lines will present a lower bound if it starts by K S or an upper bound if it starts by K I Then one number identifies the criterion an integer between and n and the following one indicates the bound s value If we denote by LB and UB respectively the lower and upper bound for k the weight of the j criterion then the successive lines should appear as follows for j n the order is arbitrar
32. esentation of the actions in the Results menu either choosing by Input Order or by Variability Order Since this is the result of a Monte Carlo simulation the user may see a slightly different result IRIS 2 0 User Manual 29 IRIS 2 0 C My Documentsttestl tri OF ES File Categories Criteria Actions Constraints Results Inconsistency Help CELLS Heigthfie width 35 Font size je Actions Fixed Par Bounds Constraints Results Infer Prog Indices 5 3 Editing the inputs After opening a project or creating a new one the inputs may be edited either before or after obtaining results For convenience the user may reduce the width of the cells using the control bd jas The user may change the performance values in the Actions page which also allows to insert assignment examples Section 4 2 1 For instance let us suppose that the user wished that az Was assigned to Cy To insert such an assignment example it would be necessary to click on the cell in the column ELow of row 2 and place the value 4 as the lowest category i e the category of a cannot be lower than C The user may also click does not need to click on the cell in the column EHigh in the same row since C is already the best category Actions Fixed Par Bounds Constraints 598 7 5 649 21 RIF 757 26 Assignment example for action 2 x Lower category A Cancel mo mo 4 hos 93 80 9 14 41 2n
33. ferent to any other profile Now the assignment rule can be implemented as follows to place a in a category from C e if a does not outrank b i e s a b lt then a belongs to category C otherwise e if a does not outrank b but has outranked b then a belongs to category C2 otherwise e if a does not outrank b3 then a belongs to category C3 etc Formally the rule may be written as a belongs to category C lt a S by A a S by S s asby J2h A s ajb lt h 3 3 Inference of parameter values IRIS does not require the user to indicate precise values for the criteria weights k kn and the cutting level A Rather it allows to obtain such values through an inference procedure Mousseau and Slowinski 1998 that tries to restore assignment examples The user may indicate the following constraints on the parameter values e LB and UB denote respectively a lower and an upper bound for k e Amin ANd Ama denote respectively a lower and an upper bound ford e Cvors a denotes the worst envisaged category for a and C s a its best envisaged category At Qr ky One kn Bz 2 1 Mcons denote a set of neons additional constraints These constraints define the following system of inequalities 1 kj 2 LB 1 n note this lower bound should be greater than 0 2 k 2 UB 1 n note this upper bound should be lower than 0 5 IRIS 2 0 User Manual 10 3 2 Amin note
34. grid using the same rules For instance Cost 106 is a valid name for a criterion Please note that IRIS does not prohibit setting different alternatives or criteria with equal names The user may change the number of criteria either creating new ones or deleting some of them The Criteria menu and the pop up menu offer the commands to perform this The user may also change the number of actions either creating new ones or deleting some of them The Actions menu and the pop up menu offer the commands to perform this Each action has a lower and a higher category where it may be assigned columns ELow and EHigh respectively that allow the user to indicate assignment examples Typically the column ELow contains the lowest category which is always 1 and the column EHigh contains the highest category which is 5 in the above figure If the user changes these values then the action s assignment will be constrained it becomes an assignment example For instance in the figure above one sees three assignment examples which the program highlights action 1 is assigned to category 5 the highest one action 10 is assigned to the interval of categories 3 to 4 and action 12 is assigned to category 4 To change the values in the columns ELow and EHigh the user must click using the mouse over the cell that he she wants to change The value in ELow cannot exceed the value in EHigh Hence if both values are equal to 2 and the user wishe
35. he assignment examples together with any other bounds and additional constraints that the user wishes to insert Besides inferring a combination of values for the parameters see previous section it is possible to determine the best and worst possible assignment for each action given a consistent system of constraints using linear programming for a more general approach see Dias and Cl maco 2000 e To find W a the worst assignment for an action a compatible with the constraints l hel 2 While minf s a b ZX Ak k 20 kj k 1 gt 0 variables are A kj kn dohth l1 end while 3 Wa h A very small positive constant 0 0001 is added by IRIS to this right hand side value to ensure that the inequality becomes strict We did not add it here to simplify the presentation IRIS 2 0 User Manual 11 e To find B a the best assignment for an action a compatible with the constraints 4 het l 5 While max s a b 2 ZX A k1 k 20 k Kky 1 lt 0 variables are kj kn doht h 1 end while 3 Wa h 1 Except a few rare cases see Section 3 4 1 an action a may be assigned to the range of categories that goes from W a to B a without violating any constraint The following robust conclusions valid for all the acceptable combinations of parameter values may be drawn for every ae A e a is not worse than W a e a is not better than B a Sometimes W a B a which means
36. ias L V Mousseau J Figueira J Climaco 2002 An Aggregation Disaggregation Approach to Obtain Robust Conclusions with ELECTRE TRI European Journal of Operational Research 138 332 348 Mousseau V L Dias 2002 Valued outranking relations in Electre providing manageable disaggregation procedures Cahier du LAMSADE No 189 Jan 2002 Forthcoming in European Journal of Operational Research Mousseau V J Figueira L Dias J Climaco C Gomes da Silva 2003 Resolving inconsistencies among constraints on the parameters of an MCDA model European Journal of Operational Research 143 332 348 Mousseau V Slowinski R 1998 Inferring an ELECTRE TRI Model from Assignment Examples Journal of Global Optimization 12 157 174 Roy B 1985 M thodologie multicrit re d aide a la d cision Economica Paris Roy B 1991 The outranking approach and the foundations of ELECTRE methods Theory and Decision 31 49 73 Roy B Bouyssou D 1993 Aide multicrit re la d cision m thodes et cas Economica Paris Yu W 1992 ELECTRE TRI Aspects m thodologiques et guide d utilisation Document du LAMSADE No 74 Universit Paris Dauphine IRIS 2 0 User Manual 35 Appendix A Syntax of the input file tri Although the easiest way of creating or updating input files is through IRIS the syntax of such files allows to create or edit them using a text processor or even a spreadsheet capable of saving files i
37. k 1k 20 ES kk adl Ik gt 1k320 lt gt k k ad2 Ik gt 1k20 E kk ad3 Ik gt 1k20 lt gt kk ad4 Ik gt 1k20 lt gt k k ad5 Ik gt 1k320 lt gt k2k ad7 IRIS 2 0 User Manual 22 4 3 Output After having specified all of the inputs the user may get some results The Results menu offers the following options e The Volume Computation option estimates the volume of the polyhedron of combinations of parameter values that respect all the constraints including bounds and assignment examples using Monte Carlo simulation A window appears where user may change the number of significant digits Precision and press the button Start simulation Then IRIS determines the dimension of the polyhedron and estimates its total volume Absolute volume as well as the ratio between the total volume and the volume of the polyhedron defined by the bounds on the parameters i e excluding the other explicit constraints and the assignment example constraints Volume to bounds The window must be closed to continue using IRIS button Exit IRIS Volume Computation Al ES Precision E Dimension 7 Absolute Volume 4 51E 5 Volume to bounds 0 142 Exit e The Robust Assignments option computes the inferred parameter values and assignments as well as the range of possible assignments for each action if the constraints are consistent After choosing this option the outputs area of the screen will reflect
38. le that mirrors the present contents of the IRIS window IRIS 2 0 User Manual 26 4 5 Inconsistency analysis When the constraints are inconsistent the menu option Inconsistency becomes available leading to a new window that helps the user fix the inconsistency The inconsistency analysis form is divided in two parts On the left side it shows the list of the constraints forming the inconsistent system with a number identifying each of them On the same side the user may choose the maximum number of suggestions for fixing the inconsistency by removing relaxing some of the constraints and initiate the computation using the Suggest button On the right side the results appear as a list of different manners to resolve the inconsistency by removing an increasing number of constraints First there will appear if exist proposals to remove one constrain only then proposals involving the removal of two constraints and so on until there are no more alternative manners to resolve the inconsistency or the maximum number of suggestions is reached For instance in the picture below the fifth proposal 7 8 12 refers to the removal of three constraints identified by the numbers 7 8 and 12 although a relaxation rather than deletion of the constraints is often sufficient to restore the consistency Inconsistency analysis OF x No Descr lambdk1 k2_ k3_ ka k5 lt f uw_ Quart Constraints to remove lt 1 cap s B fi 2 C
39. lue color of their label as in the figure below which also shows a situation where the outputs are outdated because of a change in the inputs This is shown by the use of a red font Results Infer Prog Indices 0 87370 12620 242 0 12620 12620 12620 12620 1262 If there is no combination of parameter values that respects simultaneously all the bounds constraints and assignment examples then there will be no ranges to depict inputs are inconsistent In these cases IRIS shows a proposal for assigning all the actions such that the maximum deviation is minimized this can be seen in detail in the Inference Program page The assignment examples that are not restored appear in red color as in the figure below The inconsistency analysis module may help the user in these cases see section 4 5 below Actions Fixed pe4 gt Results Inferred constraints Infer Prog Actior ELow EHigh 1 4 3 2 INFERRED CONSTRAINTS PAGE This page only presents information it displays the linear constraints corresponding to the assignment examples IRIS 2 0 User Manual 25 4 3 3 INFER PROG PAGE This page only presents information it displays the linear program corresponding to the inference problem indicating which constraints are violated when they are inconsistent The rightmost column indicates the deviation between the inferred solution and each of the constraints If a value in that column is strictly greate
40. n performance at multiple dimensions criteria to a set of predefined ordered categories using a pessimistic concordance only variant of the ELECTRE TRI method Rather than demanding precise values for the ELECTRE TRI parameters IRIS allows to enter constraints on these values namely assignment examples that it tries to restore It adds a module to identify the source of inconsistency among the constraints when it is not possible to respect all of them at the same time On the other hand if the constraints are compatible with multiple assignments for the actions IRIS allows to draw robust conclusions by indicating the range of assignments for each action that do not contradict any constraint INESC Coimbra April 2003 IRIS 2 0 User Manual 2 Index MTOR cc E E E T A E E ayers naaatts 2 1 Getting started Obtaining the IRIS Software ee ceeecesecesseceseeseeeseeeeneesaeeeaeeesaeseaeeeaeseaeenaeee 3 2 A brief oVerview Of IRIS ei arse rd soo tease teats 4 24 gt What is newim IRIS Zocalo 5 3 Methodolo ty e ia e eate E AAEE taa 6 3 1 The sorting problematis oireeni ta o eeh 6 3 2 ELECTRE TR erroni Hae ti deere We Stee hea tial ie E ETE eee We 6 3 2 1 Definition of the outranking relation 0 0 eee eeeeeeseeeseeeseeeseecscecaecaecesecsseesseeeseeeseeeseeeees 7 3 2 2 Assienment TUNE 5 32 21 e i an pada tien ated See deteict na 9 3 3 Inference of parameter Values iii A cata 9 3 4 Robust assignment ranges est e seeis
41. n simple text ASCII format The first character in each line determines the data it contains or determines that the line contains a comment if the character is c This does not mean however that IRIS accepts data in arbitrary order Rather IRIS expects to read data in a sequence that cannot be changed e IRIS recognizes the input file as being from version 2 by a first line like the following one otherwise it will treat it as being a version 1 file c version 2 e The first non comment line should start with a t to indicate the size of the problem If n is the number of criteria t is the number of categories and m is the number of actions alternatives then the line should have the following format with spaces or tabs separating the numbers t n t m e The next non comment line should start with a d to indicate the direction of the criteria followed by neri numbers separated by spaces or tabs Each of these numbers may take the value 1 when the corresponding criterion is to maximize preference increases with the performance or 1 when it is to minimize preference decreases with the performance e g a cost d I l I l 1 1 e Then IRIS expects lines starting with a p to present the performances associated with the profiles that separate the categories The first profile will be the one separating the lowest worst category from the second lowest The last profile will be the one separating the s
42. new alternative action Delete Deletes an alternative action prompting the user to choose which one Erase Examples Removes all the assignment examples the actions are not deleted only the constraints imposed on them IRIS 2 0 User Manual 45 CONSTRAINTS Menu e Insert Adds a new constraint e Delete Deletes a constraint prompting the user to choose which one Note that the constraint number zero norm cannot be deleted RESULTS Menu e Volume Computation Provides an estimate of the volume of the polytope formed by the combinations of parameter values that respect all the constraints bounds and assignment examples e Robust Assignments Updates the outputs solving the inference problem and determining the assignment ranges robustness analysis e by Input Order Sorts the actions by their input number e by Variability Order Sorts the actions by decreasing variability order INCONSISTENCY Menu This menu is available only when the constraints are inconsistent It activates the inconsistency analysis form HELP Menu e Online Manual Opens the on line manual A default browser must be installed e How to Get Help Briefly explains how to get help e About Provides information on the IRIS version Available pop up menus These menus are accessible either using the right button of the mouse or using a special key present in some keyboards e Actions page A menu gives access to the options in the
43. nt information to minimize the maximum constraint violation Section 3 3 e the category where each action is assigned to according to the inferred values A kj k Je highlighting the assignment examples that were not restored e for each constraint an indication of whether it is violated and by how much e alist of sets of constraints that if removed yield a consistent system see Section 3 6 The proposed procedure is designed to be used interactively i e the output at a given iteration is used to guide the revision of the input for the following iteration The procedure can start with very little information Each iteration will provide opportunity to add delete or modify a specific supplementary constraint Adding only a single piece of information at each allows to better understand its effect on the results This process should aim at progressively reducing the set of accepted combinations of parameter values until the end users decision makers problem owners are satisfied with the results precision and yet comfortable with and confident about the constraints introduced The final outputs of the procedure are e a set of constraints and assignment examples defining a set of acceptable combinations of parameter values e an inferred combination of parameter values defining a model in a precise manner e a precise assignment or range of assignments for each action in A that is robust with respect to the constraints inserted
44. ordance starts to increase when the difference in favor of b becomes larger than u b and attains its minimum 1 when the difference in favor of b becomes equal to or greater than v b v bn U by 0 A The use of the parameters u b is optional If these parameters are not used then IRIS considers the value by default u b 0 25 p b 0 75 v b as advocated by Mousseau and Dias 2002 The n single criterion discordance indices one for each criterion are then aggregated into a global multicriteria discordance index considering the maximum of these values Fica IRIS 2 0 User Manual 9 Finally the credibility of the statement a S b is given by s a bn c a b 1 d a b The cutting level A is a threshold that indicates whether the credibility is significant or not a outranks b a S by gt slab X 3 2 2 ASSIGNMENT RULE The pessimistic variant of ELECTRE TRI implemented in IRIS assigns each action a to the highest category C such that a outranks b To use such a rule the following conditions have to be taken into account when defining the set of profiles B e g b is better than g b 1 Vje 1 n bn dominates b for h 1 f e a S bo a outranks the worst profile bo V aie A e a S b a does not outrank the best profile b V a e A e ifa sA is indifferent to a profile b e B i e a S by A bn S ai then a will not be indif
45. r than zero then the constraint is being violated and this is highlighted using the red color as shown below The inferred solution shown in the Results page is the one that minimizes the greatest of these values Results Inferred constraints Infer Prog 0 004 0 005C 0 0050 0 4801 0 4801 0 4801 0 4801 0 4801 0 395 0 0050 0 4801 1 5E 5 0 4751 0 004 0 005 nan VV TV TV Tv Ty LB lambda UB lambda LB k1 UB k1 LB k2 UB k2 LB k3 STAV A Y A gt Y 4 3 4 INDICES PAGE This page only presents information it indicates the geometric mean of the number of possible assignments per action when the constraints are consistent and its variation relative to the previous computation 4 4 Results report The user may produce a report text file on the outputs that have been computed by selecting FilelReport or button al It is not necessary to supply an extension since the program will automatically append the extension rpt This file indicates see also Appendix C e the inferred assignment as well as its best and worst category for each action if the input is consistent e the inference mathematical program and e the solution to the inference program which corresponds to the inferred assignment This text file may then be formatted as in a text processor or may even be read by a spreadsheet program If the user chooses FilelPrint form he she will obtain a bitmap fi
46. rPPOO0O0OOrrrr oOo0O0OO0PrPPrOoO0oO0o00o0o00o00ool o oorroo00o0o000o0o0o0ol oo RPRBRO0OO0O0O0O0O0O0O00Oo0l o0Oo0OoO BOHOKBROKROKROUOD WO H WO H U INFERRED SOLUTION lambda kil k2 k3 k4 k5 0 99505 0 00495 0 32498 0 01 0 33003 0 33003 IRIS 2 0 User Manual 44 Appendix D Menu structure Available menus in the bar FILE Menu New Creates a new problem asking for its dimensions Open Opens a problem reading the inputs from disk Report Creates a file containing the computed results Save Data Saves the current inputs on disk considering the current file s name and location Save Data As Saves the current inputs on disk allowing the user to specify the file s name and location Print Form Prints a copy of the IRIS window Print Setup Allows the user to define the printer s settings Exit Terminates the program CATEGORIES Menu Split Splits a category prompting the user to choose which one into two categories The user has to specify suitable profiles for the two categories Merge Merges two consecutive categories the user chooses the lower one into a single one The user does not need to edit the profiles since the merged category inherits the lower bound of the lower category and the upper bound of the higher category CRITERIA Menu Insert Adds a new criterion Delete Deletes a criterion prompting the user to choose which one ACTIONS Menu Insert Adds a
47. rameter values Wan Ae that is inferred from the current information Section 3 3 e for each action the category were it belongs according to those inferred values e for each action the range of categories where it might be assigned without violating any constraint Section 3 4 which also allows to see which actions are more affected by the imprecision e for each action a sample combination of parameter values compatible with each category in its range e g if an action a could be assigned to any category between C and C the user could analyze four combinations of parameter values each one leading to a different category this analysis is particularly useful for the worst and best categories in the range since it may suggest new constraints on the corresponding extreme parameter values e the relative size volume of the set of parameters that satisfy all the constraints e the geometric mean of the number of categories where each action may be assigned IRIS 2 0 User Manual 13 If the system is inconsistent In this case there will not exist any combination of values for the variables A k k that satisfies the system 1 8 The interaction should aim at restoring the system s consistency by removing or at least relaxing one or more constraints To guide the user in this task several results may be computed e a central combination of parameter values Mk kn that is inferred from the curre
48. rom a file and then may be changed or typed in by the user To open an gt existing file choose FilelOpen or button lt and locate the file The default extension is tri To create a new file choose FilelNew or button EL and insert the number of actions alternatives the number of criteria and the number of categories for your problem The program allows to add or delete criteria actions or categories later The caption of the window indicates the name of the current inputs file In the present version of the program there is a limit of 20 criteria The number of actions is limited only by the amount of memory To save the current file choose FilelSave Data As or button E which allows the user to define the location and name of the file or choose FilelSave Data to save it under its current name and location An alternative to creating and editing the inputs file using IRIS which is the most natural option is to create or edit that file using a text processor given the syntax presented in Appendix A Appendix B shows how to import data from a spreadsheet like Excel The inputs area which may be enlarged or reduced contains four pages e Actions To edit the performances of the actions on the multiple criteria and optionally to set some assignment examples e Fixed Par To edit the performances that define category bounds profiles and to edit the criteria thresholds associated with these bounds e Bounds To edit the
49. rovements suggested by users of IRIS 1 0 1 1 and from a recent theoretical development see ii below i New integer programming routines were incorporated in the software thus allowing it to run the inconsistencies analysis module without resorting to an external solver IRIS 1 0 depended on the presence of the LINGO solver from Lindo Systems Inc which is now no longer necessary However computations may be slower in this new version ii IRIS 2 can work with veto thresholds thus allowing to model discordance in the construction of outranking relations It uses the variant S outranking relation proposed by Mousseau and Dias 2002 allowing the user to work with single v or double v and u discordance thresholds per criterion iii Action names and criteria names may be edited and saved These names may be arbitrarily chosen any string including alphanumerical characters 0 9 and a z spaces and symbols such as 1 Etc whereas in IRIS 1 actions and criteria were identified by numbers For instance Cost 10 6 is a valid name for a criterion iv The input files tri extension have a new format in order to contain information about the discordance related thresholds and the action and criteria names However IRIS 2 is able to read files created by IRIS 1 Conversely IRIS 1 is able to read files created by IRIS 2 but information about discordance related thresholds and the action an
50. s to change both values to 3 he she IRIS 2 0 User Manual 19 must change EHigh first The Actions menu contains a command Erase Examples to remove all the assignment examples by setting ELow equal to 1 and EHigh equal to the number of categories 4 2 2 FIXED PARAMETERS PAGE When working in the Fixed Par page the user may edit the performances of the profiles reference actions often fictitious that separate two consecutive categories as well as the thresholds associated with the criteria which may vary from profile to profile When there are 1 categories there will exist t profiles Actions Fixed Par Bounds Constraints 300 1000 300 Use vj Use uj The performances of the profiles may be directly input in the corresponding cells A row staring with g bi refers to the i th profile Profile g b separates the two worst categories denoted categories 1 and 2 profile g b2 separates categories 2 and 3 and so forth The rows starting with qi refer to the indifference thresholds associated with the i th profile and the rows starting with pi refer to the preference thresholds for the i th profile The preference threshold for a given criterion cannot be less than the corresponding indifference threshold By default IRIS is prepared to accept veto thresholds see figure above To disable veto for a particular criterion the user may place the value of zero which is hidden for the veto threshold of that
51. sor or a spreadsheet saving the file in text format The syntax of the inputs file usually with a tri extension is described and exemplified in Appendix A IRIS 2 0 User Manual 34 Credits e Wei Yu 1992 published the ELECTRE TRI method in his PhD thesis under the supervision of Bernard Roy LAMSADE Univ Paris Dauphine France e Vincent Mousseau and Roman Slowinski 1998 were the originators of the mathematical program to infer parameter values from assignment examples e Luis Dias and Joao Climaco 2000 proposed the computation of the worst and best categories for the actions given a set of constraints on the parameter values to derive robust conclusions e Luis Dias Vincent Mousseau Jos Figueira Jo o Cl maco and Carlos Gomes da Silva Dias et al 2002 Mousseau et al 2003 have developed the methodology that IRIS is based on combining parameter inference with robustness analysis and inconsistency analysis see Section 3 That research has been partially supported by Portuguese French cooperation project 328J4 ICCTI French Embassy at Portugal e Luis Dias and Vincent Mousseau have defined the functionality and interface of IRIS e Luis Dias Carlos Gomes da Silva and Rui Louren o have performed the software engineering and programming work References Dias L C Climaco J N 2000 ELECTRE TRI for Groups with Imprecise Information on Parameter Values Group Decision and Negotiation 9 355 377 D
52. that a precise robust assignment has been found for that action despite the lack of precise values for the parameter values 3 4 1 IMPOSSIBLE ASSIGNMENTS WITHIN A RANGE It may occur that some actions a A cannot be assigned to categories which lay between W a and B a As an illustration let us consider the assignment of an action a according to four criteria 8i 82 83 84 Action a has performances that are between bz and b according to criteria g and g2 According to these criteria it would belong to C On the other hand according to criteria g3 and g4 it has performances that are between bo and b hence should belong to C If k k22 A then the first two criteria are important enough to make a fall into C3 otherwise a falls into C there is no intermediate possibility i e whatever the values for k k2 kz k4 and A it is not possible for a to be assigned to Co In the version of ELECTRE TRI presented in sections 3 1 3 2 such impossible assignments may appear only when an action compares equivalently with two consecutive profiles when discordance does not intervene C ibn 1 cj a by Vie L n lt a cannot be assigned to Cr V ki kn IRIS 2 0 User Manual 12 3 5 Interaction process to build an ELECTRE TRI model Dias et al 2002 describe an interactive process to progressively build an ELECTRE TRI model i e to define the values for the criteria weights an
53. those criteria and the differences in the evaluations small differences might be ignored whereas vary large differences may oppose a veto to the outranking In the next subsections we present the variant of ELECTRE TRI implemented by IRIS for other variants see Yu 1992 Roy and Bouyssou 1993 3 2 1 DEFINITION OF THE OUTRANKING RELATION We present here the definition of the outranking relation on AXB as proposed by Mousseau and Dias 2002 Let us introduce some more notation ek is the importance coefficient weight of criterion g which is always a positive number e g b is the indifference threshold associated with criterion g and profile b e p b is the preference threshold associated with criterion g and profile bj e u f b is the discordance threshold associated with criterion gj and profile bj e v b is the veto threshold associated with criterion g and profile by e A is the advantage of a over b on criterion g gj a 85 bn ifg j is to be maximized the more the better SE g lbr g a if g is to be minimized e cj a b is the concordance index for the assertion a S b considering criterion g c a b is the concordance index for the assertion a S b considering all the criteria e d a b is the discordance index for the assertion a S b considering criterion g e s a b is the credibility index for the assertion a S b
54. tions Fixed Par Bounds Constraints Results Inferred constraints Infer Prog Indices The fact that action azg is the one with highest variability of possible assignments invites the user to see if these possibilities may be reduced Supposing that the user considered this action as a good example for category C the following results would be reached Actions Fixed Par Bounds Constraints Results Inferred constraints Infer Prog Indices 0 8000 0 10490 390020 104980 1049 0 2950 At this point the user might be so satisfied with the low variability of the results that the process could stop The user may choose FilelReport after having computed any results If issued At this IRIS 2 0 User Manual 33 point in the example a report choose FilelReport would coincide with example 1 in Appendix E 5 8 Creating a new project To create a new project the user may choose the command FilelNew A window appears where the user indicates the dimensions of the project New Problem Number of altematives E Number of criteria 2 Number of categories 2 X Cancel After setting these dimensions the user may start editing the inputs The number of criteria actions alternatives and categories may be changed later using the Criteria Actions and Categories menus respectively An alternative to creating the inputs using IRIS is to create the inputs file using a text proces
55. upper and lower bounds of the importance coefficients weights and the cutting level lambda e Constraints To edit the explicit constraints other than bounds on the parameter values Note that the implicit constraints related to assignment examples are edited in the Actions page 4 2 1 ACTIONS PAGE When working in the Actions page the user may edit the multicriteria performances of the actions to be sorted and may insert assignment examples IRIS 2 0 User Manual 18 Actions Fixed Par Bounds Constraints Results Inferred constrain_4 gt o 5 4 5 3 5 4 5 3 5 2 5 3 5 3 5 4 5 2 4 2 4 2 4 3 4 2 4 2 The performances of the actions may be directly input in the corresponding cells The user may navigate between cells using the mouse or the keyboard arrow keys All input must be numerical either positive or negative values either integer or not the decimal point is regardless of Window s settings The performance cells cannot be blank zero values must be explicitly inserted as a number The names of the actions may be edited by clicking on the corresponding cell Action column Any string of characters may be used to name an action including alphanumerical characters 0 9 and a z spaces and symbols such as For instance Project 4 is a valid action name Criteria names may also be edited by clicking on the corresponding cell title row of the
56. ut must be numerical either positive or negative values either integer or not the decimal point is The performance cells cannot be blank zero values must be explicitly inserted as a number The user may change the number of categories either creating new ones by splitting existing categories or deleting some of them by merging consecutive categories The Categories menu and the pop up menu offer the commands to perform this The user may also change the number of criteria either creating new ones or deleting some of them The Criteria menu and the pop up menu offer the commands to perform this 4 2 3 BOUNDS PAGE When working in the Bounds page the user may edit the upper and lower bounds of the cutting level lambda and the weights ki refers to the weight of the i th criterion File Categories Criteria Actions Constraints Results Inconsistency Help ea CELLS Heigthfi6 width 28 Font size a Actions Fixed Par Bounds Constraints Results inferred constrain 4 gt flambajki k2 k3 ka k5 fke kz 0 01 0 01 0 01 On on 0 01 0 01 JUB 0 99 049 049 049 049 049 0 49 O49 IRIS 2 0 User Manual 21 Bounds may be directly input in the corresponding cells The user may navigate between cells using the mouse or the keyboard arrow keys All input must be numerical in the interval 0 1 the decimal point is The upper bounds should not of course be lower than the corresponding lower bounds Zero
57. y KS j UB KI j LB e Then IRIS expects one line starting with K N followed by a number Meons indicating the number of additional constraints on the criteria weights not counting with the con straint that their sum is equal to one This line is mandatory even if there are no additional constraints then 7 should be set to zero K N Ncons If neons iS greater than zero IRIS expects n n lines starting with K g or K e IRIS 2 0 User Manual 37 A constraint Qtg A Q k O k gt B should be coded as KG Oy 0 ahs On B A constraint Qo Q k On kn lt B should be coded as K g 0 07 sh On B A constraint Qo Q k On kn B should be coded as Ke 0 Ql eZ OL B e Then IRIS expects two lines one starting with L m followed by a lower bound for the cutting level lambda and the other starting with L M followed by an upper bound for the same parameter Lm Anin LM Amar e Finally IRIS expects one line starting with n followed by n lines containing the names of the n criteria Example version 2 this is the file for testl tri Size of the problem 5 4 20 Directions of preference 1 1 Profiles 1 10 60 2 8 20 3 25 30 Thresholds 1 4 N N BwWNHRFOBWDNHE OB WN CDWOODNDVWWDOCOCVNDCOOCOO oo0oorooo0oo0rooooro ol WO OW O10 CO BW 00 Nor WwW OMAIDUBWNRFROPWWWWWNHNNND MAYAN BWNHER O W Us 0910010 c c d
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