## Fuzzy Decision Procedures with Binary Relations: Towards A Unified TheoryIn decision theory there are basically two appr~hes to the modeling of individual choice: one is based on an absolute representation of preferences leading to a ntDnerical expression of preference intensity. This is utility theory. Another approach is based on binary relations that encode pairwise preference. While the former has mainly blossomed in the Anglo-Saxon academic world, the latter is mostly advocated in continental Europe, including Russia. The advantage of the utility theory approach is that it integrates uncertainty about the state of nature, that may affect the consequences of decision. Then, the problems of choice and ranking from the knowledge of preferences become trivial once the utility function is known. In the case of the relational approach, the model does not explicitly accounts for uncertainty, hence it looks less sophisticated. On the other hand it is more descriptive than normative in the first stand because it takes the pairwise preference pattern expressed by the decision-maker as it is and tries to make the best out of it. Especially the preference relation is not supposed to have any property. The main problem with the utility theory approach is the gap between what decision-makers are and can express, and what the theory would like them to be and to be capable of expressing. With the relational approach this gap does not exist, but the main difficulty is now to build up convincing choice rules and ranking rules that may help the decision process. |

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### Contents

V | 1 |

VI | 7 |

VII | 11 |

IX | 15 |

X | 19 |

XI | 23 |

XII | 31 |

XIII | 32 |

XXXI | 119 |

XXXII | 122 |

XXXIII | 133 |

XXXIV | 137 |

XXXV | 138 |

XXXVI | 140 |

XXXVII | 150 |

XXXVIII | 153 |

### Other editions - View all

Fuzzy Decision Procedures with Binary Relations: Towards A Unified Theory Leonid Kitainik Limited preview - 2012 |

Fuzzy Decision Procedures with Binary Relations: Towards A Unified Theory Leonid Kitainik No preview available - 2012 |

### Common terms and phrases

a-cuts aggregation antireflexive antisymmetric antisymmetric relations Antitransitivity axioms basic dichotomies bicomponents binary preference relations Chapter choice functions choice rules components composition law condition contains Contraposition conventional corresponding crisp binary relation crisp relation crisp subsets crisp von Neumann decision problems decision rules decision theory decision-making definition dichotomous contensiveness digraph efficiency equality equivalent Example families FDDP FDDP'a FI'a FNMZS formula fuzzy binary relation fuzzy decision procedures fuzzy inclusions fuzzy set theory fuzzy subsets fuzzy versions FZSC GETCHA GOCHA hence implies incontensive induced crisp choice inequality interval invariant Kitainik L.Zadeh lattice Lemma Let us denote Let us suppose mapping Modus Ponens monotonicity Morgenstern Solution multifold fuzzy choice non-dominated alternatives non-empty partition polynomial preference domain preference relations preordering problem Proof properties Proposition prove ranking domain reflexive represent representation resp respect restricted environment Roubens satisfying semilattice specialization Stable Core t-norm Theorem top point transitive universal environment

### Popular passages

Page 241 - Bezdek, JC, Spillman, B. and Spillman, R. (1978). A fuzzy relation space for group decision theory, Fuzzy Sets and Systems 1, 255-268.

Page 244 - SA Orlovski (Eds.): Optimization Models Using Fuzzy Sets and Possibility Theory. D. Reidel Publishing Co., 1987.

Page 244 - soft' measure of consensus in the setting of partial (fuzzy) preferences, European Journal of Operational Research 34: 3 1 6-325.

Page 241 - A fuzzy relation space for group decision theory", Fuzzy Sets and Systems 1, 255-268. Bezdek, J., Spillman. B., and Spillman, R. (1979), "Fuzzy relation spaces for group decision theory: An application".

Page 244 - Axiomatics and Properties of Fuzzy Inclusions, Scientific Works of the Institute for System Studies, Issue 10 (1986) (in Russian) . 11.

Page 243 - Logic and the Treatment of Fuzzy Relations and of Generalized Set Equations. In: E.-P.Klement, Ll.Valverde (eds.) "Twelfth International Seminar on Fuzzy Set Theory", Linz, 1990.