General transitivity conditions for fuzzy reciprocal preference matrices

A reciprocal fuzzy matrix (relation) is a non-negative matrix Q = {qij} such that qij + qji = 1 for all i,j ∈ {1,2,..., n}. We define general transitivity conditions (named FG-transitivities) for fuzzy reciprocal preference relations and show that they generalize some well-known transitivities. We also study relationships of these conditions with two models of rational preferences (the so-called "utility" model and the "multidimensional" model).

[1]  T. Tanino.  Fuzzy preference orderings in group decision making , 1984 .

[2]  Bruce L. Stern,et al.  Research for Marketing Decisions , 1978 .

[3]  Zbigniew Switalski.  Rationality of fuzzy reciprocal preference relations , 1999, Fuzzy Sets Syst..

[4]  K. Nakamura.  Preference relations on a set of fuzzy utilities as a basis for decision making , 1986 .

[5]  Richard A. Brualdi,et al.  Generalized transitive tournaments and doubly stochastic matrices , 1992 .

[6]  Tetsuzo Tanino,et al.  Fuzzy Preference Relations in Group Decision Making , 1988 .

[7]  Vincenzo Cutello,et al.  An Extension of the Axioms of Utility Theory Based on Fuzzy Rationality Measures , 2000 .

[8]  P. Fishburn.  Binary choice probabilities: on the varieties of stochastic transitivity , 1973 .

[9]  Andrew Whinston,et al.  Fuzzy Sets and Social Choice , 1973 .

[10]  M. Fedrizzi,et al.  On the issue of consistency in dynamical consensual aggregation , 2002 .

[11]  Janusz Kacprzyk,et al.  Social Choice under Fuzziness: A Perspective , 2000 .

[12]  Janusz Kacprzyk,et al.  Analysis of consensus under intuitionistic fuzzy preferences , 2001, EUSFLAT Conf..

[13]  Francisco Herrera,et al.  Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations , 1998, Fuzzy Sets Syst..

[14]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[15]  Zbigniew Switalski,et al.  Transitivity of fuzzy preference relations - an empirical study , 2001, Fuzzy Sets Syst..

[16]  Marc Roubens,et al.  Linear fuzzy graphs , 1983 .

[17]  Jon Lee,et al.  More facets from fences for linear ordering and acyclic subgraph polytopes , 1994, Discret. Appl. Math..

[18]  Peter C. Fishburn.  Decomposing weighted digraphs into sums of chains , 1987, Discret. Appl. Math..

[19]  T. Tanino.  On Group Decision Making under Fuzzy Preferences , 1990 .

[20]  Peter C. Fishburn,et al.  Binary Probabilities Induced by Rankings , 1990, SIAM J. Discret. Math..

[21]  J. Bezdek,et al.  Fuzzy relation spaces for group decision theory: An application , 1979 .

[22]  K. Basu.  Fuzzy revealed preference theory , 1984 .

[23]  J. Fodor,et al.  Preferences and Decisions under Incomplete Knowledge , 2000 .

[24]  Philippe Vincke,et al.  Multicriteria Decision-aid , 1993 .

[25]  A. Tversky.  Intransitivity of preferences. , 1969 .

[26]  Niels Blunch,et al.  Paul E. Green and Donald S. Tull: Research for Marketing Decisions . Prentice-Hall, Inc., Englewood Cliffs, N. ,J. 1966. , 1967 .

[27]  Richard E. Quandt,et al.  A Probabilistic Theory of Consumer Behavior , 1956 .

[28]  Antoine Billot,et al.  Economic Theory of Fuzzy Equilibria , 1992 .

[29]  Martin Grötschel,et al.  Facets of the linear ordering polytope , 1985, Math. Program..

[30]  H. Nurmi.  Approaches to collective decision making with fuzzy preference relations , 1981 .

[31]  T. Dridi.  Sur les distributions binaires associées à des distributions ordinales , 1980 .

[32]  Bernard Monjardet,et al.  A Generalisation of Probabilistic Consistency: Linearity Conditions for Valued Preference Relations , 1988 .

[33]  J. Kacprzyk,et al.  Multiperson decision making models using fuzzy sets and possibility theory , 1990 .

[34]  B. Baets,et al.  Twenty years of fuzzy preference structures (1978–1997) , 1997 .

[35]  Pavel Yu. Chebotarev,et al.  Characterizations of scoring methodsfor preference aggregation , 1998, Ann. Oper. Res..