Instituto de Engenharia de Sistemas e Computadores
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1. outranks a profile bpe B denoted S bp if it can be considered at least as good as the latter 1 a is not worse than given the evaluations performances of a and b at the n criteria If a is not worse than b in every criterion then it is obvious that a S bp However if there are some criteria where a is worse than bp then a may outrank b or not depending on the relative importance of those criteria and the differences in the evaluations small differences might be ignored In the next subsections we present a concordance only version of the outranking relation and the pessimistic ELECTRE TRI assignment rule which characterize 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 concordance only definition of the outranking relation on AxB Let us introduce some more notation is the importance coefficient weight of criterion g which is always a positive number qj b is the indifference threshold associated with criterion g and profile bj pj b is the preference threshold associated with criterion g and profile A is the advantage of a over b on criterion gj 8 8j bj is to be maximized the more the better M 2 if g C is to be minimized cj d bj is the concordance index for the assertion a S considering2. 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 The family of ELECTRE 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 m number of actions number of criteria 1 number of categories Am set of actions G g g4 set of criteria real valued functions on A Ci set of ordered categories C is the worst one C is the best one Bz b bj set of profiles reference actions that separate consecutive categories IRIS 1 0 User Manual 4 Each category C is limited by two reference actions profiles b is its upper limit and 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 An action
3. the first one constraining the action s assignment from below 1 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 7 or if the second of these numbers is lower than t then these actions will belong to the set of assignment examples If we denote by g a the performance action a at the g criterion its worst envisaged category and by Coes ai its best envisaged category then there should appear lines as follows a i 8 224 gai Chest Gi 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 T Then one number identifies the criterion an integer between and and the following one indicates the bound s value If we denote by LB and UB respectively the lower and upper bound for the weight of the j criterion then the successive lines should appear as follows for j 1 n the order is arbitrary KS j UB KI j LB Then IRIS expects one line starting with K followed by a number indicating the number of additional constraints on the criteria weights not counting with the constraint that their sum is equal to one This line is mandatory even if there are no addi
4. 4 1 5 115171 571 4 2 5 t s 2242514985 235 345 48525 54 27445 5 12572937 46 946 1 224154 935 1 3 31 R 293 2 YN NN 4 CO CO CO A CO 4 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 fob p i The user may change the performance values in the Actions page which also allows him her to insert assignment examples Section 4 2 1 For instance let us suppose that the user wished that a was assigned to C3 To insert such an assignment example it would be necessary to click on the cell in the column EHigh of row 2 and place the value 3 as the upper category 1 the category of cannot be higher than C The user may also click on the cell in the column ELow in the same row and place the value 3 as the lowest category 1 the category of cannot be lower than C5 although the result obtained previously already guarantees that Actions Par ip 35 8167 1870 4 5 16414559875 52 5 3 4 2 1 135860 64921 45 5 n c example for action 2 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 cuttin
5. 8 1 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 by adding a new one To guide the user in this task several results may be computed central combination of parameter values A k k J that is inferred from the current information Section 3 3 foreach action the category where it belongs according to those inferred values IRIS 1 0 User Manual 9 for each action the range of categories where it might be assigned without violating any constraint Section 3 4 which also allows us to see which actions are more affected by the imprecision for each action a sample combination of parameter values compatible with each category in its range e g if an action could be assigned to any category between C and Cs 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 the relative size volume of the set of parameters that satisfy all the constraints the geometric mean of the number of categories where each action may be assigned If the system is inconsistent In this case there will not exist any combination of value
6. IRIS 1 0 User Manual S Size of the problem 2 5 3 10 z i oo oo oo eio 8 Thresholds 1 2 0 0 3 0 0 4 0 0 5 0 0 1 0 0 2 0 0 3 4 0 0 5 0 0 19 Actions 0 0 0 0 0 1 3 0 0 0 0 0 1 3 a2 0 0 0 0 0 1 3 0 0 0 0 0 1 3 0 0 0 0 0 1 3 0 0 1 3 0 0 0 0 0 1 3 0 0 0 0 0 1 3 0 0 0 0 0 1 3 ag 0 0 0 0 0 1 3 41 gt 2 35 IRIS 1 0 User Manual 36 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 worst category W a the inferred category 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 i W a B aj The third part of the report presents the constraints to the inference mathematical program that minimizes 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 o
7. 005 0 1 73 0 005 4 00 7 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 three possible ways to restore the consistency either to remove constraint 2 1 that belongs to category C or lower or to remove constraint 5 i e that k2 0 or to remove constraint 3 i e that as belongs to category C Closing this window returns the user to the main IRIS window Inconsistency analysis Gi x Constraints to remove 2 gt B 4 Max sti f ax suggestions 5 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 1 in Appendix C The user may select the name and location of the report file IRIS 1 0 User Manual 28 5 7 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 Number of alternatives E Number of criteria NN Number of categories 2 X Cancel After setting these
8. 3 ERENCE PROGRAM escr d1 d2 d4 d5 d6 LB lambda B lambda B k1 k1 k2 k2 k3 k3 k4 k4 k5 k5 k6 k6 k7 k7 A Co alpha lambda 1 1 gt qp nd 1 1 1 1 1 1 1 1 1 1 1 1 C CX gt C29 Or HO CO OO OOOO CO gt DE OD DE 763 69 me es ae gt OOOO Ore OO Ror eS TO UOCE eve eS NFERR 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ON ED SOLUTI ambda 596 k1 k2 k3 0 005998 0 39601 0 40001 oor p p wor He wor or 0 a torar EE OOO OO O OO OOS cp EC T C906 2907 69 H RV QS CO C0 C C2 gt Co QO OL Q 6b C ds 4 Qs OLB o k4 k5 k6 k7 0 005998 0 005998 0 17999 0 005998 38 IRIS 1 0 User Manual 39 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 lo
9. behaves equivalently in the confrontation with two consecutive profiles Vje L n cannot be assigned to 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 1 to define the values for the criteria weights and 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 recall Section 3 3 on the criteria weights and the cutting level besides fixed values for the actions performances the profiles and the indifference and preference 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 0 126 0 49 and the cutting level e g 0 515420 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 kn that satisfy the system 1
10. 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 menus associated with them To access these menus the user just has to click on the right button of the IRIS 1 0 User Manual 13 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 from a file and then may be changed or typed in by the user To open an existing file choose FilelOpen or button e and locate the file The default extension is To create a new file choose FilelNew or button and insert the number of actions alternatives the number of criteria and the number of categories for your problem The program allows us to add or to 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 15 criteria The number of actions is limited only by the amount of memory To save the current file choose FilelSave Data As or button which allows the user to define the location and the 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 o
11. introduced The final outputs of the procedure are a set of constraints and assignment examples defining a set of acceptable combinations of parameter values an inferred combination of parameter values defining a model in a precise manner a precise assignment or range of assignments for each action in A that is robust with respect to the constraints inserted IRIS 1 0 User Manual 10 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 3 6 Dealing with inconsistencies It may occur that after introducing some constraints the system of inequalities 1 k 2 LB 1 Q k UB j 1 n 3 A E Amin 4 A Amax 5 e a bo sel 1 kj T c2 ai bc 1 k2 i tly a DC pt k A ai A 6 CI a bo a k 2 ai b a j k5 a bo a 2 _ 7 A kn 2 lt 1 8 k kot 1 becomes inconsistent i e there does not exist any combination of values for the parameters 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 2002 One of these methods uses mixed int
12. is presented in the Indices page Results Inferred constraints Infer Prog Indices Results Inferred constraints Infer Prog Indices GEOMETRIC MEAN FOR No CATEGORIES Including examples 1 357 variation 1 236 47 7 k2 ks k5 ke 0 83 0 10 0 28 0 19 0 10 0 10 0 10 0 10 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 Cs Obviously that is inconsistent with the constraints imposed so far as IRIS will state when the user introduces this example via the Actions page as exemplified above and re calculates the results IRIS 1 0 User Manual 27 Results Robust Assignments The assignments corresponding to the inferred parameter values are presented in red color in the cases where the examples have not been restored and ag below IRIS 1 0 C My Documents File Categories Criteria Actions Constraints Results Inconsistency Help gt 8 CELLS Heigthfi6 Width 24 H Results Inferred constraints Infer Prog 67 1370 0 14 5 59 8 7 5 60 649 21 61 7 757 3 6 17 1 57 1 42 251 49 8 5 345 48 9 25 44 578 17 54 274 45 ni 297 468 46 3 k2 ks ks 7 24 6 648 36 87 0 596 0 005 0 336 0 400 0 005 0
13. k2Ek4 k2 k5 k22k6 k22k7 0 1 1 0 0 0 1 0 Bounds lambda M 0 99 m 0 6 IRIS 1 0 User Manual 34 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 example xls Performance data 2 action so so so so so r s To import these data the user may proceed as follows 1 Start IRIS Create a new file indicating 10 actions 5 criteria and the number of categories Section 5 7 2 3 4 Save the file choosing its location and name e g example tri Section 5 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 Copy the data in cells B3 F12 from example xls to the cells B20 F29 in the file example tri Save example tri keeping the text tab delimited format and close that file Re open example tri in IRIS it now contains the copied data
14. 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 a 15 not worse than W a a 15 not better than Sometimes W a B a which means 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 that lay between W a and As an illustration let us consider the assignment of an action a according to four criteria gi gx 83 24 IRIS 1 0 User Manual 8 Action a has performances that are between 6 and b according to criteria g and g According to these criteria it would belong to On the other hand according to criteria g3 and g4 it has performances that are between and 5 hence should belong to If k k2 A then the first two criteria are important enough to make fall into otherwise a falls into there is no intermediate possibility i e whatever the values for k2 k3 k4 and A it is not possible for a to be assigned to C In the version of ELECTRE TRI presented in sections 3 1 3 2 such impossible assignments may appear only when an action
15. the actions order at any time even after the results are computed IRIS 1 0 C My Documents MCahltinf tri Ioj File Categories Actions Constraints Results Inconsistency Help CELLS 15 Font size Actions Fixed Pe4 gt Results Infer Prog Indices fer c2 63 cs o 0 87370 12620 24250 12620 12620 12620 12620 1262 Select cells to see solution for the respective assignment IRIS 1 0 C My Documents Cahlti nf tri File Categories Actions Constraints Results Inconsistency Help CELLS Heigh ie Font size 6 Results Infer Prog Indices 017 0 315 0 307 0 307 0 017 0 017 0 01 7 0 87370 1 2620 24250 12620 12620 12620 12620 1262 The Results page uses color to indicate the range of possible assignments for each action robustness analysis 1 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 IRIS 1 0 User Manual 19 instance a28 in the figure above when a28 is good enough to be better than C7 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 i
16. 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 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 1 0 C My DocumentsNXCahlti nf tri File Categories Actions Constraints Results Inconsistency Help CELLS Heigh 1e 28 Font size e Actions Fixed Par Beunds Constraints Results Infer Prog Indices k2 k5 ks 0 0175 0 315 0 307 0 307 0 017 0 017 0 017 87370 12620 242 0 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 Heiath 16 _ 4 widh s2 Font size 3 4 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
17. 049 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 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 simply type lt 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 IRIS 1 0 C My DocumentsNXC
18. B WN Ot pm qp pu oc OO VUES DOWNWANDWOWNWAHANDWOWN WAN CO WN O IRIS 1 0 User Manual 33 Actions only one assignment example a2 Category 3 id gl g2 g3 g4 g6 97 LowC Ds 67 19 1 16 14 595 35 60 64 20 61 75 11 qa Die 22 225 49 235 34 48 229 5T 8 7 2 255 46 21 2 64 18 3 69 ZO cel Eg 1 9 535 80 52 ZT 534 42 60 56 74 44 65 dd us 4 000 1001 BP OO 0 00 LP J o mo 0 OB OQ BWD WW CU 010101010101 010101010101 01010101 01 01 C0 wo Upper bounds on weights kl k7 0 49 1 0 49 4 4 4 4 4 4 K K K K K K K bounds on weights 1 720 01 NANNAN ANNAA Additional constraints N 6 there are 6 constraints stating that k22k1 k2Ek3
19. IRIS the syntax of such files allows us to create or edit them using a text processor or even a spreadsheet capable of saving files in 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 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 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 The next non comment line should start with a d to indicate the direction of the criteria followed by 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 1 1 171 17 1 Then IRIS expects 1 1 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 second best category from the bes
20. ISSN 1645 4847 Instituto de Engenharia de Sistemas e Computadores Institute of Systems Engineering and Computers INESC Coimbra NA IRIS Interactive Robustness analysis and parameters Inference for multicriteria Sorting problems Version 1 0 User Manual Lu s DIAS Carlos GOMES da SILVA and Vincent MOUSSEAU Documents of INESC Coimbra No 1 January 2002 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 inabili
21. Manual 21 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 S It is not necessary to supply an extension since the program will automatically append the extension rpt This file indicates see also Appendix C the inferred assignment as well as its best and worst categories for each action if the input is consistent the inference mathematical program and 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 file that mirrors the present contents of the IRIS window 4 5 Inconsistency analysis When the constraints are inconsistent the menu option Inconsistency becomes available leading to a new window that helps the user to 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
22. a eU doe eet e e E RERO UE 7 3 4 1 Impossible assignments within a range sss tenente ettet tenente tenente eene 7 3 5 Interaction process to build an ELECTRE TRI model esee tenente tnnt ten 8 3 6 Dealing with inconsist nCles reete ere t eae eae te t e Ree tee ede e dede 10 Software presentation eth rte eet eR bed cob ee i cea dee ese e Or ete e nece 12 4 1 General eee re tee ee p er tet m lt iem perd 12 ARR A NR 13 2 2 1 Actions EUR Uere a cemere e M bU ee ie o uper ee RES 13 42 2 Fixed parameters page edere tup ee teneo edet Ped Dro SRI a ek 14 4 2 3 Bounds 4 2 4 Constraints page 4 3 Output eee A Wes 31 Results page secre E Ete e Aeg te ccs 4 32 Inferred constraints Dette d nie e RE e prets 20 435 page IARE Re ER ete 434 Indices page eene ERU DURO I EE b Un iere Re ERREUR S 4 4 Results report 4 5 Inconsistency analysis 55A stepby step example 3 re orent 23 Opening projJecEs ett tee te ee Ae et eee e ER ette ties 5 2 Obtaming results eet re e 5 31 Editing the anputs ERROR EE EO ERR 5 4 Saving the data 5 5 Obtaining new results 5 5 Analyzing inconsistencies i 5 6 Producing report oeste eR RERO AU ERR ERE RE E EH 5 7 Creating new projectin
23. ahlti nf tri File Categories Actions Constraints Results Inconsistency Help CELLS Heigh is Width 28 Font size p Actions Fixed Par Bounds Constraints ___ k3 ks k5 ke kz lt gt UN EHI IRIS 1 0 User Manual 17 In the above example the constraints 247 to ad6 force kz to have a value that is not less than any of the other weights kj tlko20 adl 1k2 1k320 k 22k 3 ad2 k 1k420 ad3 Ik5 1k 5 50 T k22k 5 ad4 klkg20 kozkg ad5 1 gt 16720 ko5k ad7 4 3 Output After having specified all of the inputs the user may get some results The Results menu offers the following options 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 1 excluding the other explicit constraints and the assignment example constraints Volume to bounds The window must be closed
24. ances If the value is 7 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 input 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 actions either creating new ones or deleting some of them The Actions 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 IRIS 1 0 User Manual 16 IRIS 1 0 C My DocumentsNXCahlti nf tri File Categories Actions Constraints Results Inconsistency Help Actions Fixed Bounds Constraints lambafkt k3 ks ks ke 001 0 01 001 001 001 001 001 0 99 049 049 049 049 049 049
25. are The directory where IRIS is located should contain The executable program irisl exe and or irislsi exe lighter version that does not offer inconsistency analysis The Manual directory containing the manual files main man htm etc The file iss_res Ing containing a script for inconsistency analysis not required by iris1si exe The Lingo optimization software files not required by irislsi exe Lingcall dll LingODBC dll and Lingxcel dll All these files should be copied from the user s Lingo installation The license lic file not required by irislsi exe containing information about Lingo s license which should be copied from the users Lingo installation IRIS may run using the free student demo version of Lingo that can be downloaded from http www lindo com However that version is capable of solving problems of modest size only in terms of the number of constraints Furthermore the directory C Windows System should contain the file Lingodll dll not required by irislsi exe that should be copied from the user s Lingo installation
26. as in the figure below The inconsistency analysis module may help the user in these cases see section 4 5 below IRIS 1 0 User Manual 20 IRIS 1 0 C My DocumentsSXCahlti nf tri File Categories Actions Constraints Results Inconsistency Help Wea CELLS Heigthfi6 221 widthf28 Fontsize s Actions Fixed Pe4 gt Results Inferred constraints Infer Prog Acior ELow EHigh ct c2 cs o h 4 3 2 INFERRED CONSTRAINTS PAGE This page only presents information it displays the linear constraints corresponding to the assignment examples 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 greater 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 IRIS 1 0 C XMy 1 File Categories Actions Constraints Results Inconsistency Help 0 004 0 0050 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 0050 or IRIS 1 0 User
27. assignment examples Robust Assignments Updates the outputs solving the inference problem and determining the assignment ranges robustness analysis byInput Order Sorts the actions by their input number 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 Online Manual Opens the on line manual A default browser must be installed How to Get Help Briefly explains how to get help 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 Actions page A menu gives access to the options in the criteria and actions menus described just above and an option for getting specific help 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 Bounds page A menu gives access to an option for getting specific help Constraints page A menu gives access to the options in the constraints menu described just above and an option for getting specific help Results and Infer Prog pages A menu gives access to an option for getting specific help IRIS 1 0 User Manual 41 Appendix E Files used by the IRIS softw
28. 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 IRIS 1 0 User Manual 15 with the criteria that may vary from profile to profile When there are f categories there will exist 1 1 profiles IRIS 1 0 C My DocumentsNCahlti nf tri DE File Categories Actions Constraints Results Inconsistency Help We als CELLS ro C CO 0 92 30 a EN aw The performances of the profiles may be directly input in the corresponding cells 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 The last row in the grid indicates if the preference increases or decreases with the perform
29. cation Save Data As Saves the current inputs on disk allowing the user to specify the file s name and location Print 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 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 1 0 User Manual 40 CONSTRAINTS Menu Insert Adds a new constraint Delete Deletes a constraint prompting the user to choose which one Note that the constraint number zero norm cannot be deleted RESULTS Menu 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
30. criterion g c ajb is the concordance index for the assertion a 5 bp considering all the criteria A is the cutting level For each criterion 1 a concordance index indicates how much that criterion agrees with the hypothesis S which is computed as follows 0 fA pj by c j ai by e p j bn p j bn if Aj lt 1 2 4 IRIS 1 0 User Manual 5 The concordance is maximum 1 when is better than b or is worse but by a small difference up to qj 5 When a is worse than the concordance starts to decrease when the difference in favor of by becomes larger than q bn and attains its minimum 0 when the difference in favor of by becomes equal to or greater than p b q by 0 Aj 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 aj by Y Kj where we assume that Y EIS Since we are not dealing with discordance we will interpret this concordance index as the credibility of the statement a S bp The cutting level is a threshold that indicates whether the credibility is significant or not a outranks bp a S bj c dibn ZA 3 2 2 ASSIGNMENT RULE The pessimistic variant of ELECTRE TRI implemented in IRIS assigns each acti
31. 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 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 IRIS 1 0 User Manual 29 Credits Wei Yu 1992 published the ELECTRE TRI method in his PhD thesis under the supervision of Bernard Roy LAMSADE Univ Paris Dauphine France Vincent Mousseau and Roman Slowinski 1998 were the originators of the mathematical program to infer parameter values from assignment examples Luis Dias and Joao Cl maco 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 Luis Dias Vincent Mousseau Jos Figueira Jo o Climaco and Carlos Gomes da Silva Dias et al 2002 Mousseau et al 2002 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 projects 328J4 and 500B4 ICCTI French Embassy at Portugal Luis Dias and Vincent Mousseau have defined the functional
32. e files Lingcall dll LingODBC dll Lingxcel dll and license lic from the Lingo installation to the folder where irisl exe is located copy the file Lingodll dll from the Lingo installation to the directory C Windows System 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 4351 239 824692 Rua Antero de Quental 199 Phone 351 239 851040 3000 033 Coimbra Portugal C O Luis M C Dias LDias G inescc pt IRIS page in the Internet www4 fe uc pt Imcdias iris htm IRIS may run using the free student demo version of Lingo which can be downloaded from http www lindo com However that version is capable of solving problems of modest size only in terms of the number of constraints IRIS 1 0 User Manual 2 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 a company into categories that define incentive packages etc IRIS implements a methodology developed by Luis Dias Vincent Mous
33. eger programming continuous and 0 1 variables to compute a succession of sets of constraints 51 S S such that 1 Vie 1 p if the constraints S are removed from system 1 8 then it becomes consistent 2 Vi 1 p izj S S Vi efl p i lt j 151 lt 183 EN If removing set of constraints 5 from the system 1 8 makes it become consistent then either S c S 1 1 or ISI IS Jl Each one of the sets 5 S5 Sp 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 iteration may then continue as explained in the previous section The method to compute these sets is the following one Setp l Solve the 0 1 programming problem min S5 jy ZX Akp kn 20 ki ko k 1 20 Vz 0 1 IRIS 1 0 User Manual 11 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 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 t
34. en the system Z X ye 0 is consistent and the optimal value for the variables A kj satisfies all the constraints Otherwise if the minimum 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 IRIS 1 0 User Manual 7 3 4 Robust assignment ranges Let us consider again the system ZX A K k 7 0 1 1 introduced in the previous section which represents all the assignment examples besides 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 assignments for each action given a consistent system of constraints using linear programming for a more general approach see Dias and Cl maco 2000 Tofind W a the worst assignment for an action a compatible with the constraints l h 1 2 While min c a bj ZX k ks 20 ki kn l 20 variables are A ky kn doh 1 end while 3 Wai h To find B a the best assignment for an action a compatible with the constraints 4 t I 5 While max c a bi A ZX A k j ks 20 k k 1 lt 0 variables are ky kn doh h 1 end while 3 W ai h 1 Except a few rare cases
35. es 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 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 1 0 User Manual 3 3 Methodology 3 1 The sorting problematic Roy 1985 defines four problematics categories of problems in multicriteria decision aiding description problematic the purpose of the analysis is to describe the decision situation in a formal language in terms of actions criteria and evaluations choice problematic the purpose of the analysis is to select one action or a set of x actions ranking problematic the purpose of the analysis is to rank the actions by order of preference 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
36. f Window s settings The performance cells cannot be blank zero values must be explicitly inserted as a number 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 to columns ELow and EHigh respectively 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 that 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 if the user wishes to change both values to 3 he she must change EHigh first The Actions menu contains a command Erase Examples to remove all the
37. 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 This option is not available in the version Iris1si This module uses the LINGO optimization software from Lindo Systems Inc namely the DLLs Lingodll dll LingODBC dll Lingcall dll and Lingxcel dll IRIS 1 0 User Manual No Descr __ k4 Quant Constraints toremove 4 cup M 1 p 2 gt 22 IRIS 1 0 User Manual 23 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
38. g eet outage WIEN WW eet e bU Credits d ette er RE REN RS 29 Referencess d e REC RU UA RR de s 29 Appendix A Syntax of the input file 11 tenente nente tenerent ete tenen tenete teen Appendix B Importing data from MS Excel Appendix C Syntax of the report file rpt Appendix D Menu structure seen Appendix E Files used by the IRIS software IRIS 1 0 User Manual 1 1 Getting started Obtaining the IRIS Software IRIS runs on Windows 95 98 Me computers The monitor should be at least VGA 640x480 with 16 colors It occupies very 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 i To install IRIS unzip the contents of the file irisl zip to a new folder with a location and a name of your choice The package includes two programs see Appendix E irisl is the software described in this manual iris1si is a lighter version of iris1 that does not include the module that performs inconsistency analysis and hence does not interact with Lingo To use 1 the following instructions are not needed to run iris1si it is necessary to install Lingo the optimization software from Lindo Systems Inc if it has not been installed yet copy th
39. g 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 1 0 User Manual 26 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 corresponds to the latter option which asks for the file s name and location and allows him her 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 ResultslRobust Assignments The assignment example that a5 belongs to C causes a reduction 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 and an indicator the geometric mean of the number of categories in a range
40. ghts and cutting level has a dimension of 4 55x107 Considering only the combinations that respect the bounds defined in the Bounds page about 74 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 ResultslIRobust 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 C4 Recall Section 4 3 to know how to interpret these results and interactively calculate some other ones For instance action a5 was assigned to C but might also have been assigned to C or Cs 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 presentation of the actions in the Results menu either choosing by Input Orderor by Variability Order IRIS 1 0 User Manual 25 IRIS 1 0 C My Documents Test1_tri File Categories Actions Constraints Results Inconsistency Help 7 CELLS Heigthfi6 4 widthf20 Fontsie s Actions Fixed Par Bounds Constraints Results Infer Prog Indices 2 1 5 135 850 64921 3 t 5 20661 7 75736
41. hat all would be zero if the system 1 8 was consistent Since the system 1 8 is not consistent the optimal solution to the above problem will contain several ie 1 z Let S 2 1 2 1 Then removing the constraints indexed by S from 1 8 would result in a consistent system Setp 2 Solve the 0 1 programming problem min 2 M yp y50 20 Kk tkot k 1 Dies Yi 88 1 20 Vz 0 1 This mathematical program is equal to the former except the introduction of a new constraint Eie 5 Yi lt 5 1 This constraint prohibits the former optimal solution or a superset of that solution A set 52 is formed from the new optimal solution as explained for the case of Sj Set p 3 add the constraint Eis y S5 1 etc The process stops as soon as a pre defined number of sets is reached or when the 0 1 programming problem which means that there are no more alternative ways to restore the consistency of 1 8 IRIS 1 0 User Manual 12 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
42. 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 E My Computer ed 3 Floppy amp 48 Audio CD D 53 My Briefcase TRI parameters amp constraints tri To follow this example the user should locate the file test1 tri which comes with IRIS The path and name of the file will appear in the caption of the IRIS window IRIS 1 0 C My Documents Test1 tii IRIS 1 0 User Manual 24 5 2 Obtaining results After opening a project using FilelOpen or res or after creating a new one using FilelNew the user may start editing the file and obtaining results Choosing Results Volume Computation allows him her to compute the relative volume of parameter polyhedron that respects the constraints imposed so far i e the constraints which state that k2 is not lower than any other k j 2 according to the data in the Constraints 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 x Precision Dimension 7 Absolute Volume 4 55E 5 Volume to bounds 0 143 Exit In this example the 7 dimension polyhedron of acceptable values for the wei
43. ity and interface of IRIS Luis Dias and Carlos Gomes da Silva inconsistency analysis were responsible for the software engineering and programming work References Dias L C Cl maco J N 2000 ELECTRE TRI for Groups with Imprecise Information on Parameter Values Group Decision and Negotiation 9 355 377 Dias L V Mousseau J Figueira J Climaco 2002 An Aggregation Disaggregation Approach to Obtain Robust Conclusions with ELECTRE TRI European Journal of Operational Research vol 138 332 348 Mousseau V J Figueira L Dias J Cl maco C Gomes da Silva 2002 Resolving inconsistencies among constraints on the parameters of an MCDA model to appear in the European Journal of Operational Research Mousseau V Slowinski R 1998 Inferring an ELECTRE TRI Model from Assignment Examples Journal of Global Optimization vol 12 157 174 Roy B 1985 M thodologie multicrit re d aide 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 1 0 User Manual 30 Appendix A Syntax of the input file tri Although the easiest way of creating or updating input files is through
44. on a to the highest category such that a outranks 5 To use such a rule the following conditions have to be taken into account when defining the set of profiles B g b is better than g bn 1 Vj amp 1 n bn dominates for 1 t a 5 bo a outranks the worst profile bo V a A a S a does not outrank the best profile bj a amp A is indifferent to a profile i e S bn b S aj then a will not be indifferent to any other profile Now the assignment rule can be implemented as follows to place a in a category from C if a does not outrank b i e c a jb lt then a belongs to category otherwise if a does not outrank b gt but has outranked then a belongs to category otherwise if a does not outrank b then a belongs to category etc Formally the rule may be written as a belongs to category C S by aiS by 2 lt IRIS 1 0 User Manual 6 3 3 Inference of parameter values IRIS does not require the user to indicate precise values for the criteria weights kn and the cutting level Rather it allows him her 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 LB and UB denote a lower and an upper bound fo
45. r 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 Actions To edit the performances of the actions at the multiple criteria and optionally to set some assignment examples Fixed Par To edit the performances that define category bounds profiles and to edit the thresholds associated with the criteria Bounds To edit the upper and lower bounds of the importance coefficients weights and the cutting level lambda 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 1 0 User Manual 14 IRIS 1 0 C XMy DocumentsSCahlti nf tri File Categories Actions Constraints Results Inconsistency Help 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 o
46. r kj respectively Amin and denote a lower and an upper bound for amp respectively Cyorsi ai denotes the worst envisaged category for a and its best envisaged category e Oy ki Os kn 2 lt 1 denote a set of ncons additional constraints These constraints define the following system of inequalities 1 k LB j 1 n note this lower bound should be greater than 0 2 k UBj j 1 n note this upper bound should be lower than 0 5 3 Amin note this lower bound should not be lower than 0 5 4 A Amax note this upper bound should be lower than 5 ej a d boost xi kj T a Deos aj 1 C a E sd 4 pi k A aj amp A 6 a be ky 2 ai bc a j k5 ee Or a E 2 a j amp A T A eg kj os kn 2 Z 1 Ncons to which we add 8 k ko k 1 Let us write the constraints 1 7 in a more compact matrix notation as ZX Aky kn 20 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 if exist that satisfies all the constraints which implies restoring all the assignment examples with greatest slack min o 8 ZX Akn kn 20 k k 1 the variables are ox kj kn If the minimum x its optimal value is zero or less th
47. r the existing slacks 1f Error is negative Let us denote each constraint as following the pattern BoA P n3 INFERENCE PROGRAM Descr lambda lt gt RHS Error label E Boe Bu lt Bs eror The last part of the report presents the optimal solution A 25s kn to the inference program INFERRED SOLUTION lambda kl kn A kj ke The format of this results file makes it convenient to be read by a text processor or a spreadsheet 37 IRIS 1 0 User Manual Example 1 consistent system E B e me SULTS E INPUT FIL C MMy Documents NTest2 tri R p oO p n em p 44 a 4 Worst Cat PROGRAM alpha lambda INFERENCE Error P lt gt RHS k7 kl k2 k3 k4 k5 k6 LB lambda 1 UB lambda 1 INFERRED SOLUTION lambda kl 0 103 0 289 0 19601 0 103 0 103 0 103 0 103 0 897 IRIS 1 0 User Manual Example 2 inconsistent system INPUT FILE C R A CO D C 2 gt 3 C 2 23 8 gt 5 L I 1 0 UJ UJ UJ UJ UJ UU UU UU UJ UJ UJ CJ w CTION MMy Documents Test3 tri ESULTS Worst Cat Inferred Cat Best Cat 5 4 5 4 4 4 4 5 4 4 3 4 4 4 3 4 4 4 4 4 4 3 4 4
48. rs Inference for multicriteria Sorting problems This tool has been built to support the assignment of actions alternatives projects candidates described by their evaluation 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 January 2002 Contents 1 Getting started Obtaining the IRIS Software sees tette tenente tente tenente tenen 1 2 A briebovetview of IRIS o eee boten aee aaa beeen 2 3 Methodology uh Re dE eU RCRUM 3 33 The s rtmg problematic ee PRI NEAR 3 32 EEBCTRE IRL cete peres c es 9 3 2 1 Definition of the outranking relation sR ss ues 4 3 2 2 Assignment rule sss e ae B 59 3 3 Inference of parameter values eere RU 6 3 4 Robust assignment ranges ss e vere ep eee e
49. s for the variables kn that satisfies the system 1 8 The interaction should aim at restoring the system s consistency by removing or al least relaxing one or more constraints To guide the user in this task several results may be computed a central combination of parameter values A k k that 1s inferred from the current information to minimize the maximum constraint violation Section 3 3 for each action the category where it belongs according to the inferred values A k k highlighting the assignment examples that were not restored for each constraint an indication of whether it is violated and by how much a list 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 us 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
50. s 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 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 28 to C5 The actions that are assignment examples can easily be identified by the blue 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 IRIS 1 0 C XMy DocumentsSXCahlti lambd k fka k5 ks MERE 0 035 0 2426 0 035 0 217 0217 0 217 0035 0 87370 1 2620 24260 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
51. seau Jos Figueira and Jo o Climaco presented in Dias et al 2002 see also Section 3 which is based on the ELECTRE TRI method The inconsistency analysis method is presented in Mousseau et al 2002 see also Section 3 The main characteristics or IRIS are IRIS implements a concordance only variant of the pessimistic ELECTRE TRI 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 IRIS accepts assignment 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 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 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 categori
52. t 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 je criterion then the successive lines should appear as follows the id_number is ignored but must be present p id_number g b gobi 8n b1 p id number g b2 822 8n b2 p id number gi bi i 8 2 1 En br 1 Afterwards IRIS expects n t 1 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 1 1 1 the second number identifies the criterion an integer between and the third number indicates the indifference threshold and the fourth indicates the preference threshold If we denote by q b and p b respectively indifference and preference threshold associated IRIS 1 0 User Manual 31 to the J criterion given the performance of the r profile then the successive lines should appear as follows rzl t 1 j n 5 r J qib 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 integer identifies the action followed by numbers indicating the performances of the action at the multiple criteria Finally there should appear two integer numbers between and 1
53. tional constraints then cons should be set to zero K N n cons If neons is greater than zero IRIS expects lines starting with K g or A constraint A cy kn should be coded as Kg T Gf B A constraint e kn B should be coded as Kg a t be B A constraint e e c should be coded as Ke h p IRIS 1 0 User Manual 32 Finally IRIS expects two lines one starting with L m followed by a lower bound for the cutting level lambda and the other one starting with L M followed by an upper bound for the same parameter Lm LM Example Size of the problem 7 criteria 5 categories 25 actions 7 5 25 Directions of preference maximize criteria 1 2 6 amp 7 minimize criteria 3 4 amp 5 1 1 1 1 1 1 1 Profiles 1 10 2 0 3 8 4 25 Thresholds qi 1 pl 2 for q2 4 p2 6 for q3 1 p3 3 for q4 1 p4 2 for 5 0 5 3 for q6 2p6 0 for al 47 7 9 for al 1 1 1 bh 1 profiles l profiles l profiles l profiles l profiles rofiles rofiles l 1 S S S 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 BPP gt gt SP 40 C C0 CO PO PO PO PO PO Or FF FF BS EF 015 O
54. to continue using IRIS button Exit IRIS Volume Computation _ X Precision 3 Dimension ri Absolute Volume 4 51E 5 Volume to bounds 0 142 Exit 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 the inputs The by Input Order option instructs IRIS to sort the actions by their input number 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 IRIS 1 0 User Manual 18 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
55. ty to use the software or accompanying written materials including this report Technical support INESC Coimbra may provide technical support via e mail Gecretaria 9 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 IRIS Antero de Quental 199 3000 033 Coimbra Portugal Tel 239851040 Fax 239824692 IRIS Interactive Robustness analysis and parameters Inference for multicriteria Sorting problems Version 1 0 User Manual Lu s DIAS Carlos GOMES da SILVA Vincent MOUSSEAU Coimbra INESC Coimbra 2002 4 41p Documentos do INESC Coimbra ISSN 1645 4847 IRIS Interactive Robustness analysis and parameters Inference for multicriteria Sorting problems Version 1 0 User Manual Lu s DIAS Carlos GOMES da SILVA 3 and Vincent MOUSSEAU 1 INESC Coimbra 2 Faculdade de Economia Universidade de Rua Antero de Quental 199 Coimbra 3000 033 Coimbra PORTUGAL Av Dias da Silva 165 3004 512 Coimbra PORTUGAL 3 Escola Superior de Tecnologia e Gest o 4 LAMSADE Universit Paris Dauphine Instituto Polit cnico de Leiria Place du Mar chal De Lattre de Tassigny 2401 951 Leiria PORTUGAL 75775 Paris Cedex 16 FRANCE Abstract This document is the User Manual for the decision support software IRIS Interactive Robustness analysis and paramete
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