## Fuzzy Preference Modelling and Multicriteria Decision SupportThe encounter, in the late seventies, between the theory of triangular norms, issuing frorn stochastic geornetry, especially the works of Menger, Schweizer and Sklar, on the one band, and the theory of fuzzy sets due to Zadeh, 10n the other band has been very fruitful. Triangular norms have proved to be ready-rnade mathematical rnodels of fuzzy set intersections and have shed light on the algebraic foundations of fuzzy sets. One basic idea behind the study of triangular norms is to solve functional equations that stern frorn prescribed axioms describing algebraic properties such as associativity. Alternative operations such as rneans have been characterized in a similar way by Kolmogorov, for instance, and the rnethods for solving functional equations are now weil established thanks to the efforts of Aczel, among others. One can say without overstaternent that the introduction of triangular norms in fuzzy sets has strongly influenced further developrnents in fuzzy set theory, and has significantly contributed to its better acceptance in pure and applied rnathematics circles. The book by Fodor and Roubens systematically exploits the benefits of this encounter in the- analysis of fuzzy relations. The authors apply functional equation rnethods to notions such as equivalence relations, and various kinds of orderings, for the purpose of preference rnodelling. Centtal to this book is the rnultivalued extension of the well-known result claiming that any relation expressing weak preference can be separated into three cornponents respectively describing strict preference, indifference and incomparability. |

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### Contents

III | 1 |

IV | 2 |

V | 4 |

VI | 5 |

VII | 6 |

IX | 8 |

X | 10 |

XI | 11 |

LXIV | 95 |

LXV | 98 |

LXVI | 99 |

LXVII | 100 |

LXVIII | 101 |

LXX | 102 |

LXXI | 103 |

LXXIII | 104 |

XIII | 12 |

XV | 13 |

XVI | 14 |

XVII | 15 |

XVIII | 16 |

XXII | 17 |

XXV | 18 |

XXVII | 20 |

XXIX | 21 |

XXXI | 24 |

XXXII | 28 |

XXXIII | 31 |

XXXIV | 33 |

XXXV | 35 |

XXXVI | 37 |

XXXVII | 38 |

XXXVIII | 39 |

XXXIX | 42 |

XL | 43 |

XLI | 45 |

XLII | 50 |

XLIII | 51 |

XLIV | 53 |

XLV | 54 |

XLVI | 56 |

XLVII | 57 |

XLVIII | 62 |

XLIX | 64 |

L | 67 |

LI | 68 |

LII | 69 |

LIII | 71 |

LIV | 72 |

LVI | 73 |

LVII | 74 |

LIX | 78 |

LX | 81 |

LXI | 82 |

LXII | 85 |

LXIII | 87 |

LXXIV | 105 |

LXXVI | 107 |

LXXVII | 108 |

LXXIX | 110 |

LXXX | 112 |

LXXXI | 117 |

LXXXII | 127 |

LXXXIV | 135 |

LXXXV | 140 |

LXXXVI | 143 |

LXXXVII | 145 |

LXXXVIII | 149 |

LXXXIX | 150 |

XC | 156 |

XCI | 158 |

XCII | 159 |

XCIII | 162 |

XCIV | 163 |

XCV | 165 |

XCVI | 166 |

XCVII | 170 |

XCVIII | 171 |

XCIX | 172 |

C | 175 |

CI | 176 |

CIII | 189 |

CV | 198 |

CVI | 199 |

CVII | 204 |

CIX | 216 |

CX | 218 |

CXI | 221 |

CXII | 223 |

CXIII | 229 |

CXIV | 234 |

CXV | 236 |

239 | |

253 | |

### Other editions - View all

Fuzzy Preference Modelling and Multicriteria Decision Support J.C. Fodor,M.R. Roubens Limited preview - 2013 |

Fuzzy Preference Modelling and Multicriteria Decision Support J.C. Fodor,M.R. Roubens No preview available - 2014 |

Fuzzy Preference Modelling and Multicriteria Decision Support J.C. Fodor,M.R. Roubens No preview available - 2010 |

### Common terms and phrases

A-cut Aczel aggregation operator alternatives antisymmetric associated automorphism axiomatic axioms Chapter characterized Choquet integral CNM operators condition consider continuous Archimedean t-norm continuous t-norm Corollary corresponds crisp binary relations crisp relation Definition Dubois and Prade equivalence relation equivalent example exists an automorphism finite Fodor functional equations fuzzy sets given gj(a holds idempotent implies inequality interval order irreflexive Lemma Lukasiewicz M(xi means monotonic Morgan triple negatively transitive nilpotent obtain obviously ordinal sum Ovchinnikov partial T-order point of view positive t-norm preorder procedure Proof properties Proposition quasiorder R-implication ranking reflexive Renault R9 Roubens S-completeness satisfied scoring function Section semitransitive similarity relation strict negation strict preference strong negation strongly complete Suppose symmetric T-asymmetry T-classes t-conorm T-similarity T-transitive T-transitive valued binary Table transitive closure transitive relation unit interval v(Pi valuation valued binary relation valued relations weighted zero divisors

### Popular passages

Page 240 - Ranking methods based on valued preference relations: a characterization of the net flow method. European Journal of Operational Research 60 (1992a) 61-68 2.

Page 239 - Comparison of fuzzy sets on the same decision space", Fuzzy Sets and Systems.

Page 241 - Preference, in: J. Kacprzyk and M. Fedrizzi, Eds., Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, Kluwer Academic publishers, Dordrecht, 1990, pp 172-185. [19] RR Yager, "On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making," IEEE Transactions on Systems, Man and Cybernetics, Vol.