To the Decision Deck platform UTA GMS /GRIP plugin Piotr Zielniewicz Poznan University of Technology, Poland 2nd Decision Deck Workshop February 21-22,

Slides:



Advertisements
Similar presentations
Modellistica e Gestione dei Sistemi Ambientali A tool for multicriteria analysis: The Analytic Hierarchy Process Chiara Mocenni University of.
Advertisements

5.4 Basis And Dimension.
Multi‑Criteria Decision Making
Multiple-criteria ranking using an additive value function constructed via ordinal regresion : UTA method Roman Słowiński Poznań University of Technology,
Preference Elicitation Partial-revelation VCG mechanism for Combinatorial Auctions and Eliciting Non-price Preferences in Combinatorial Auctions.
1 Helsinki University of Technology Systems Analysis Laboratory Robust Portfolio Modeling for Scenario-Based Project Appraisal Juuso Liesiö, Pekka Mild.
Helsinki University of Technology Systems Analysis Laboratory RICHER – A Method for Exploiting Incomplete Ordinal Information in Value Trees Antti Punkka.
Behavioral Finance Uncertain Choices February 18, 2014 Behavioral Finance Economics 437.
10/11/2001Random walks and spectral segmentation1 CSE 291 Fall 2001 Marina Meila and Jianbo Shi: Learning Segmentation by Random Walks/A Random Walks View.
Copyright © 2006 Pearson Education Canada Inc Course Arrangement !!! Nov. 22,Tuesday Last Class Nov. 23,WednesdayQuiz 5 Nov. 25, FridayTutorial 5.
The Rational Decision-Making Process
Dynamic lot sizing and tool management in automated manufacturing systems M. Selim Aktürk, Siraceddin Önen presented by Zümbül Bulut.
Preference Analysis Joachim Giesen and Eva Schuberth May 24, 2006.
Introduction to Management Science
Inferences About Process Quality
MADM Y. İlker TOPCU, Ph.D twitter.com/yitopcu.
Solve Systems of Equations By Graphing
Presented by Johanna Lind and Anna Schurba Facility Location Planning using the Analytic Hierarchy Process Specialisation Seminar „Facility Location Planning“
I can solve systems of equations by graphing and analyze special systems.
ELearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Introduction to Value Tree Analysis eLearning resources / MCDA team Director.
STOCHASTIC DOMINANCE APPROACH TO PORTFOLIO OPTIMIZATION Nesrin Alptekin Anadolu University, TURKEY.
1 Chapter 8 Sensitivity Analysis  Bottom line:   How does the optimal solution change as some of the elements of the model change?  For obvious reasons.
1 1 Slide © 2004 Thomson/South-Western Chapter 17 Multicriteria Decisions n Goal Programming n Goal Programming: Formulation and Graphical Solution and.
Lecture # 2 Review Go over Homework Sets #1 & #2 Consumer Behavior APPLIED ECONOMICS FOR BUSINESS MANAGEMENT.
SOLVING SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.
Multi-Criteria Decision Making by: Mehrdad ghafoori Saber seyyed ali
USING PREFERENCE CONSTRAINTS TO SOLVE MULTI-CRITERIA DECISION MAKING PROBLEMS Tanja Magoč, Martine Ceberio, and François Modave Computer Science Department,
Decision map for spatial decision making Salem Chakhar in collaboration with Vincent Mousseau, Clara Pusceddu and Bernard Roy LAMSADE University of Paris.
Jinsong Guo Jilin University, China Background  Filtering techniques are used to remove some local inconsistencies in the search algorithms solving.
Analyzing the Problem (Outranking Methods) Y. İlker TOPCU, Ph.D twitter.com/yitopcu.
Ellsberg’s paradoxes: Problems for rank- dependent utility explanations Cherng-Horng Lan & Nigel Harvey Department of Psychology University College London.
3.1 System of Equations Solve by graphing. Ex 1) x + y = 3 5x – y = -27 Which one is the solution of this system? (1,2) or (-4,7) *Check (1,2)Check (-4,7)
EASTERN MEDITERRANEAN UNIVERSITY Department of Industrial Engineering Non linear Optimization Spring Instructor: Prof.Dr.Sahand Daneshvar Submited.
Preference Modelling and Decision Support Roman Słowiński Poznań University of Technology, Poland  Roman Słowiński.
1 EC9A4 Social Choice and Voting Lecture 2 EC9A4 Social Choice and Voting Lecture 2 Prof. Francesco Squintani
1 Iterative Integer Programming Formulation for Robust Resource Allocation in Dynamic Real-Time Systems Sethavidh Gertphol and Viktor K. Prasanna University.
2nd Meeting of Young Researchers on MULTIPLE CRITERIA DECISION AIDING Iryna Yevseyeva Niilo Mäki Instituutti University of Jyväskylä, Finland
Multiple-criteria sorting using ELECTRE TRI Assistant
3.1 – Solve Linear Systems by Graphing A system of two linear equations in two variables x and y, also called a linear system, consists of two equations.
Multi-objective Optimization
Helsinki University of Technology Systems Analysis Laboratory Incomplete Ordinal Information in Value Tree Analysis Antti Punkka and Ahti Salo Systems.
Applied Mathematics 1 Applications of the Multi-Weighted Scoring Model and the Analytical Hierarchy Process for the Appraisal and Evaluation of Suppliers.
COMPLEXITY. Satisfiability(SAT) problem Conjunctive normal form(CNF): Let S be a Boolean expression in CNF. That is, S is the product(and) of several.
Concept Learning and The General-To Specific Ordering
1 Ratio-Based Efficiency Analysis (REA) Antti Punkka and Ahti Salo Systems Analysis Laboratory Aalto University School of Science and Technology P.O. Box.
Preference Modelling and Decision Support Roman Słowiński Poznań University of Technology, Poland  Roman Słowiński.
What is a matroid? A matroid M is a finite set E, with a set I of subsets of E satisfying: 1.The empty set is in I 2.If X is in I, then every subset of.
Linear Programming Chap 2. The Geometry of LP  In the text, polyhedron is defined as P = { x  R n : Ax  b }. So some of our earlier results should.
Behavioral Finance Preferences Part I Feb 16 Behavioral Finance Economics 437.
Chapter 3: Linear Systems and Matrices
Preference Assessment 1 Measuring Utilities Directly
Mikko Harju*, Juuso Liesiö**, Kai Virtanen*
Flexible and Interactive Tradeoff Elicitation Procedure
CIS Automata and Formal Languages – Pei Wang
A Scoring Model for Job Selection
Roman Słowiński Poznań University of Technology, Poland
NP-Completeness Yin Tat Lee
Chap 9. General LP problems: Duality and Infeasibility
Polyhedron Here, we derive a representation of polyhedron and see the properties of the generators. We also see how to identify the generators. The results.
Polyhedron Here, we derive a representation of polyhedron and see the properties of the generators. We also see how to identify the generators. The results.
Chapter 11 Limitations of Algorithm Power
Overview Part 2 – Circuit Optimization
NP-Completeness Yin Tat Lee
Behavioral Finance Economics 437.
Multicriteria Decision Making
IME634: Management Decision Analysis
Introduction to Value Tree Analysis
Overview Functional Testing Boundary Value Testing (BVT)
Dr. Arslan Ornek DETERMINISTIC OPTIMIZATION MODELS
FITradeoff Method (Flexible and Interactive Tradeoff)
Presentation transcript:

to the Decision Deck platform UTA GMS /GRIP plugin Piotr Zielniewicz Poznan University of Technology, Poland 2nd Decision Deck Workshop February 21-22, 2008 University Paris Dauphine

2nd Decision Deck Workshop, February 21-22, Plan Problem statement Problem statement Disaggregation-aggregation (regression) approach Disaggregation-aggregation (regression) approach UTA GMS method UTA GMS method GRIP method GRIP method UTA GMS /GRIP plugin overview UTA GMS /GRIP plugin overview UTA GMS /GRIP plugin demonstration UTA GMS /GRIP plugin demonstration Conclusions and future works

2nd Decision Deck Workshop, February 21-22, Problem statement Consider a finite set A of alternatives (actions) evaluated by m criteria from a consistent family F = {g 1,...,g m } Consider a finite set A of alternatives (actions) evaluated by m criteria from a consistent family F = {g 1,...,g m } Taking into account preferences of a Decision Maker (DM), rank all the actions of set A from the best to the worst Taking into account preferences of a Decision Maker (DM), rank all the actions of set A from the best to the worst A * * * * x x x x x x * * x x * x * x x x * x x x x x

2nd Decision Deck Workshop, February 21-22, Preference model To solve a multicriteria decision problem one needs a preference model, i.e. criteria aggregation model To solve a multicriteria decision problem one needs a preference model, i.e. criteria aggregation model Traditional aggregation paradigm: Traditional aggregation paradigm: The preference model is first constructed and then applied on set A to get information about the comprehensive preference Disaggregation-aggregation (ordinal regression) paradigm: Disaggregation-aggregation (ordinal regression) paradigm: The comprehensive preference on a subset A R  A is known a priori, and a consistent preference model is inferred from this information to be applied on set A

2nd Decision Deck Workshop, February 21-22, Disaggregation-aggregation (regression) approach The preference model is a set of additive utility functions compatible with a non-complete set of pairwise comparisons of some reference actions and information about comprehensive and partial intensities of preference The additive utility function is defined on A as follows: The additive utility function is defined on A as follows: U(x) = Σ u i (x i ), i  I = {1, …, m}

2nd Decision Deck Workshop, February 21-22, The UTA GMS method (Greco, Mousseau & Słowiński 2004) B R  A R x A R is the set of pairs of reference actions compared by the DM B R  A R x A R is the set of pairs of reference actions compared by the DM The preference information is a partial preorder  on a subset of reference actions A R  A The preference information is a partial preorder  on a subset of reference actions A R  A  – weak preference (outranking) relation  – weak preference (outranking) relation for each pair (x, y)  B R x  y  „x is at least as good as y” x  y  [x  y and not y  x]  „x is preferred to y” x ~ y  [x  y and y  x]  „x is indifferent to y” A utility function is called compatible if it is able to restore all pairwise comparisons from B R (i.e. partial preorder) on A R A utility function is called compatible if it is able to restore all pairwise comparisons from B R (i.e. partial preorder) on A R

2nd Decision Deck Workshop, February 21-22, The UTA GMS method (Greco, Mousseau & Słowiński 2004) Questions: Questions:  Are any two actions x, y  A ordered in the same way by all compatible utility functions?  Is there at least one compatible utility function ordering x at least as good as y (or y at least as good as x)? A ARAR x tz w v y u DM x  yz  wy  vu  tz  uu  zx  yz  wy  vu  tz  uu  z preference information analyst All instances of preference model compatible with preference information BRBR Apply all compatible instances on A

2nd Decision Deck Workshop, February 21-22, The UTA GMS method (Greco, Mousseau & Słowiński 2004) Having answers to these questions for all pair of actions (x, y)  A x A, one gets: Having answers to these questions for all pair of actions (x, y)  A x A, one gets:  necessary weak preference relation U(x)  U(y) for all compatible utility functions  necessary weak preference relation  N, whose semantics is U(x)  U(y) for all compatible utility functions  possible weak preference relation, whose semantics is U(x)  U(y) for at least one compatible utility function  possible weak preference relation  P, whose semantics is U(x)  U(y) for at least one compatible utility function The necessary and possible weak preference relations are exploited such that one finally obtains two rankings in the set of actions: The necessary and possible weak preference relations are exploited such that one finally obtains two rankings in the set of actions:  necessary ranking (partial preorder)  possible ranking (complete and negatively transitive binary relation)

2nd Decision Deck Workshop, February 21-22, The UTA GMS method (Greco, Mousseau & Słowiński 2004) Two rankings result: necessary and possible Two rankings result: necessary and possible x y w z t u v necessary ranking possible ranking Includes necessary ranking and does not include the complement of necessary ranking x  yz  wy  vu  tz  uu  zx  yz  wy  vu  tz  uu  z preference information

2nd Decision Deck Workshop, February 21-22, The UTA GMS method (Greco, Mousseau & Słowiński 2004) For any pair of actions (x, y)  A, and for available preference information represented by B R, preference of x over y is determined by compatible utility functions U verifying set E(x, y) of constraints: For any pair of actions (x, y)  A, and for available preference information represented by B R, preference of x over y is determined by compatible utility functions U verifying set E(x, y) of constraints: U’(x)  U’(y) +   x  y U’(x) = U’(y)  x ~ y u i (x i j ) – u i (x i j-1 )  0, i = 1, …, m, j = 1, …, ω + 1 u i (x i 0 ) = 0, i = 1, …, m Σ u i (x i ω+1 ) = 1, i = 1, …, m where  is a small positive constant, and ω = m |A R  {x, y}|  (x, y)  B R E(x, y)

2nd Decision Deck Workshop, February 21-22, The UTA GMS method (Greco, Mousseau & Słowiński 2004) Given a pair of actions x, y  A Given a pair of actions x, y  A x  N y  d(x, y)  0 x  N y  d(x, y)  0 where where d(x, y) = Min {U(x) – U(y)} d(x, y) = Min {U(x) – U(y)} s.t. E(x, y) s.t. E(x, y) d(x, y)  0 means that for all compatible utility functions x is at least as good as y d(x, y)  0 means that for all compatible utility functions x is at least as good as y For any (x, y)  B R : For any (x, y)  B R : x  y  x  N y x  y  x  N y

2nd Decision Deck Workshop, February 21-22, The UTA GMS method (Greco, Mousseau & Słowiński 2004) Given a pair of actions x, y  A Given a pair of actions x, y  A x  P y  D(x, y)  0 x  P y  D(x, y)  0 where where D(x, y) = Max {U(x) – U(y)} D(x, y) = Max {U(x) – U(y)} s.t. E(x, y) s.t. E(x, y) d(x, y)  0 means that for at least one compatible utility functions x is at least as good as y d(x, y)  0 means that for at least one compatible utility functions x is at least as good as y For any (x, y)  B R : For any (x, y)  B R : x  y  x  P y x  y  x  P y

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) GRIP (Generalized Regression with Intensities of Preference) extends UTA GMS method by adopting all features of UTA GMS and by taking into account additional preference information: GRIP (Generalized Regression with Intensities of Preference) extends UTA GMS method by adopting all features of UTA GMS and by taking into account additional preference information:  comprehensive comparisons of intensities of preference between some pairs of reference actions, e.g. „x is preferred to y at least as much as w is preferred to z”  partial comparisons of intensities of preference between some pairs of reference actions on particular criteria, e.g. „x is preferred to y at least as much as w is preferred to z, on criterion g i  F”

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) DM is supposed to provide the following preference information: DM is supposed to provide the following preference information:  a partial preorder  on A R, such that  x, y  A R x  y  „x is at least as good as y” x  y  „x is at least as good as y”  =   non  -1,  =    -1  =   non  -1,  =    -1  a partial preorder  * on A R  A R, such that  x, y, w, z  A R (x, y)  * (w, z)  „x is preferred to y at least as much as w is (x, y)  * (w, z)  „x is preferred to y at least as much as w is preferred to z”  * =  *  non  * -1,  * =  *   * -1 preferred to z”  * =  *  non  * -1,  * =  *   * -1  a partial preorder  i * on A R  A R, i = 1,..., m, such that  x, y, w, z  A R (x, y)  i * (w, z)  „x is preferred to y at least as much as w is (x, y)  i * (w, z)  „x is preferred to y at least as much as w is preferred to z, on criterion g i  F” preferred to z, on criterion g i  F”  i * =  i *  non  i * -1,  i * =  i *   i * -1  i * =  i *  non  i * -1,  i * =  i *   i * -1

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) A utility function U is called compatible if it satisfies the constraints corresponding to DM’s preference information: A utility function U is called compatible if it satisfies the constraints corresponding to DM’s preference information: a) U(x)  U(y) iff x  y b) U(x) > U(y) iff x  y c) U(x) = U(y) iff x  y d) U(x) – U(y)  U(w) – U(z) iff (x, y)  * (w, z) e) U(x) – U(y) > U(w) – U(z) iff (x, y)  * (w, z) f) U(x) – U(y) = U(w) – U(z) iff (x, y)  * (w, z) g) u i (x)  u i (y) iff x  i y, i  I h) u i (x) – u i (y)  u i (w) – u i (z) iff (x, y)  i * (w, z), i  I i) u i (x) – u i (y) > u i (w) – u i (z) iff (x, y)  i * (w, z), i  I j) u i (x) – u i (y) = u i (w) – u i (z) iff (x, y)  i * (w, z), i  I

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) Moreover, the following normalization constraints should also be taken into account: Moreover, the following normalization constraints should also be taken into account: k) u i (x i * ) = 0, i  I where x i * is such that x i * = min {g i (x): x A} where x i * is such that x i * = min {g i (x): x  A} l) Σ u i (y i * ) = 1, i  I where y i * is such that y i * = max {g i (y): x A} where y i * is such that y i * = max {g i (y): x  A} Let as remark that like in UTA GMS method, constraints b), e) and i) should be written as: Let as remark that like in UTA GMS method, constraints b), e) and i) should be written as: b’) U(x)  U(y) +  e’) U(x) – U(y)  U(w) – U(z) +  i’) u i (x) – u i (y)  u i (w) – u i (z) +  where  is a small positive constant

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) If constraints a) – l) are consistent, then we get two weak preference relations  N and  P, and two binary relations comparing intensity of preference  * N and  * P : If constraints a) – l) are consistent, then we get two weak preference relations  N and  P, and two binary relations comparing intensity of preference  * N and  * P : 1.for all x, y  A, a necessary weak preference relation x  N y  min {U(x) – U(y)}  0 x  N y  min {U(x) – U(y)}  0 2.for all x, y  A, a possible weak preference relation x  P y  max {U(x) – U(y)}  0 x  P y  max {U(x) – U(y)}  0 3.for all x, y, w, z  A, a necessary relation of preference intensity (x, y)  * N (w, z)  min {[U(x) – U(y)] – [U(w) – U(z)]}  0 (x, y)  * N (w, z)  min {[U(x) – U(y)] – [U(w) – U(z)]}  0 4.for all x, y, w, z  A, a possible relation of preference intensity (x, y)  * P (w, z)  max {[U(x) – U(y)] – [U(w) – U(z)]}  0 (x, y)  * P (w, z)  max {[U(x) – U(y)] – [U(w) – U(z)]}  0 where „min” and „max” are calculated over all utility functions satisfying a) – l)

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) In order to conclude the truth or falsity of necessary and possible weak preference relations  N,  P and  * N,  * P, one can use LP In order to conclude the truth or falsity of necessary and possible weak preference relations  N,  P and  * N,  * P, one can use LP To obtain the result which is independent on the value of , one should: To obtain the result which is independent on the value of , one should: Max   subject to constraints a) – l), with b), e), i) written as b’), e’), i’) If maximal  * > 0, the set of compatible utility functions is not empty If maximal  * > 0, the set of compatible utility functions is not empty

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) Then, to verify the truth or falsity of x  P y, for any x, y  A, one should: Then, to verify the truth or falsity of x  P y, for any x, y  A, one should: Max   subject to constraints a) – l), with b), e), i) written as b’), e’), i’) b’), e’), i’) and U(x)  U(y) Maximal  * > 0  x  P y Maximal  * > 0  x  P y This means that there exists at least one compatible utility function satisfying the hypothesis U(x)  U(y)

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) In order to verify the truth or falsity of x  N y, rather than to check directly that for each compatible utility function U(x)  U(y), we make sure that among the compatible utility functions there is no one such that U(x) < U(y): In order to verify the truth or falsity of x  N y, rather than to check directly that for each compatible utility function U(x)  U(y), we make sure that among the compatible utility functions there is no one such that U(x) < U(y): Max   subject to constraints a) – l), with b), e), i) written as b’), e’), i’) b’), e’), i’) and U(y)  U(x) +  Maximal  * ≤ 0  x  N y Maximal  * ≤ 0  x  N y

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) Analogously, in order to verify the truth or falsity of (x, y)  * P (w, z) for any x, y, w, z  A, one should: Analogously, in order to verify the truth or falsity of (x, y)  * P (w, z) for any x, y, w, z  A, one should: Max   subject to constraints a) – l), with b), e), i) written as b’), e’), i’) and U(x)  U(y)  U(w)  U(z) Maximal  * > 0  (x, y)  * P (w, z) Maximal  * > 0  (x, y)  * P (w, z)

2nd Decision Deck Workshop, February 21-22, The GRIP method (Figueira, Greco & Słowiński 2006) Analogously, in order to verify the truth or falsity of (x, y)  * N (w, z) for any x, y, w, z  A, one should: Analogously, in order to verify the truth or falsity of (x, y)  * N (w, z) for any x, y, w, z  A, one should: Max   subject to constraints a) – l), with b), e), i) written as b’), e’), i’) and U(w)  U(z)  U(x)  U(y) +  Maximal  * ≤ 0  (x, y)  * P (w, z) Maximal  * ≤ 0  (x, y)  * P (w, z) The value of  * is not meaningful – the result does not depend on it The value of  * is not meaningful – the result does not depend on it

2nd Decision Deck Workshop, February 21-22, UTA GMS /GRIP plugin overview Current implementation of UTA GMS /GRIP plugin works on the first version of Decision Deck platform (1.0.2) Current implementation of UTA GMS /GRIP plugin works on the first version of Decision Deck platform (1.0.2) To verify the truth or falsity of preference relations it uses GLKP linear solver which is the part of D2 platform (GLPK plugin) To verify the truth or falsity of preference relations it uses GLKP linear solver which is the part of D2 platform (GLPK plugin) To visualize rankings of alternatives in the form of graph it uses the JGraph library implemented as additional plugin To visualize rankings of alternatives in the form of graph it uses the JGraph library implemented as additional plugin UTA GMS /GRIP plugin main features: UTA GMS /GRIP plugin main features:  add/remove alternatives to/from reference set  add/remove/edit preference information (partial preorder, comprehensive and/or partial intensities of preferences)  shows comparison of alternatives  view necessary ranking of alternatives

2nd Decision Deck Workshop, February 21-22, UTA GMS /GRIP plugin demonstration Illustrative example Illustrative example Car ranking problem

2nd Decision Deck Workshop, February 21-22, UTA GMS /GRIP plugin demonstration Illustrative example – Car ranking problem Illustrative example – Car ranking problemAlternatives:Criteria:

2nd Decision Deck Workshop, February 21-22, UTA GMS /GRIP plugin demonstration Performance matrix: Skoda Opel Ford Citroen Seat VW Price Speed Space Fuel_cons. Acceleration

2nd Decision Deck Workshop, February 21-22, Conclusions and future works The preference information used in GRIP does not need to be complete: the DM can compare only those pairs of reference alternatives on particular criteria for which his/her judgment is sufficiently certain The preference information used in GRIP does not need to be complete: the DM can compare only those pairs of reference alternatives on particular criteria for which his/her judgment is sufficiently certain Distinguishing necessary and possible consequences of preference information, GRIP answers questions of robustness analysis using all utility functions instead of a single „best-fit” utility function Distinguishing necessary and possible consequences of preference information, GRIP answers questions of robustness analysis using all utility functions instead of a single „best-fit” utility function Plugin future works: Plugin future works:  visualization of possible ranking of alternatives  resolving inconsistency in preference information  visualization of necessary and possible relations of preference intensity for the pair of alternatives  manage preference information using „classes of attractiveness”