From Preference Relations to Fuzzy Choice Functions

2011 ◽  
pp. 594-605 ◽  
Author(s):  
Davide Martinetti ◽  
Ignacio Montes ◽  
Susana Díaz
Keyword(s):  
Choice Functions ◽  
Preference Relations ◽  
Fuzzy Choice Functions

scholarly journals On a correspondence between probabilistic and fuzzy choice functions

2017 ◽  
Vol 17 (3) ◽  
pp. 247-264 ◽  
Author(s):  
Davide Martinetti ◽  
Susana Montes ◽  
Susana Díaz ◽  
Bernard De Baets
Keyword(s):  
Choice Functions ◽  
Fuzzy Choice Functions

On the Rationality of Some Crisp Choice Functions Based on Strongly Complete Fuzzy Pre-Orders

2015 ◽  
Vol 11 (01) ◽  
pp. 103-113 ◽  
Author(s):  
Siméon Fotso ◽  
Louis Aimé Fono
Keyword(s):  
Fuzzy Sets ◽  
Choice Functions ◽  
Preference Relations ◽  
Natural Computation ◽  
Weak Preference ◽  
Choice Sets

Barrett, Pattanaik and Salles [Fuzzy Sets and Systems 34 (1990) 197–212] introduced nine alternative rules for generating exact choice sets from fuzzy weak preference relations (FWPR) and four rationality properties. They showed that, when preferences are fuzzy pre-orders, most of these alternative rules (preference-based choice functions or PCFs) violate at least two rationality properties. Following in the same direction, Fotso and Fono [New Mathematics and Natural Computation 8 (2012) 257–272] characterized these PCFs and analyzed their consistency in the cases of strongly complete fuzzy pre-orders and crisp complete pre-orders. In this paper, based on results of the two previous papers, we determine to what extend the PCFs are rational with respect to the structure of the underlying relation. More specifically, for each of the nine alternative rules violating a given rationality property, we determine respectively crisp pre-orders and strongly complete fuzzy pre-orders for which the PCF satisfies the property.

Similarity of fuzzy choice functions

2007 ◽  
Vol 158 (12) ◽  
pp. 1314-1326 ◽  
Author(s):  
Irina Georgescu
Keyword(s):  
Choice Functions ◽  
Fuzzy Choice Functions

A further study on rationality conditions of fuzzy choice functions

2011 ◽  
Vol 176 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Caiping Wu ◽  
Xuzhu Wang ◽  
Yonghua Hao
Keyword(s):  
Choice Functions ◽  
Fuzzy Choice Functions

Fuzzy choice functions

1991 ◽  
Vol 8 (2) ◽  
Author(s):  
M. Dasgupta ◽  
R. Deb
Keyword(s):  
Choice Functions ◽  
Fuzzy Choice Functions

Choice Functions Generated by Mallows and Plackett–Luce Relations

2019 ◽  
Vol 15 (02) ◽  
pp. 191-213 ◽  
Author(s):  
Vidal Kamdem Tagne ◽  
Siméon Fotso ◽  
Louis Aimé Fono ◽  
Eyke Hüllermeier
Keyword(s):  
Probability Distribution ◽  
Structural Properties ◽  
Probability Distributions ◽  
Preference Relation ◽  
Choice Functions ◽  
Strong Completeness ◽  
Underlying Distribution ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
Consistency Properties

The rationality and consistency of preference-based choice functions is often studied for (fuzzy) preference relations having specific properties, such as strong completeness, transitivity, or certain properties on triplets. In this paper, we turn our attention to another type of preference relation, namely relations that are induced as pairwise marginal of an underlying probability distribution on complete rankings (permutations) of all given alternatives. Such relations are necessarily reciprocal and, depending on the underlying distribution, obey additional structural properties. More specifically, we study relations induced by two important probability distributions, the Mallows and the Plackett–Luce distribution, which are well-known in the literature on statistics of rank data. Assuming preference relations of this kind, we study seven different choice functions and their four rationality and consistency properties.

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