Relevance in Preference Structures

2013 ◽  
pp. 117-125 ◽  
Author(s):  
Camilo Franco ◽  
Javier Montero ◽  
J. Tinguaro Rodriguez
Keyword(s):  
Preference Structures

A plea for the use of Łukasiewicz triplets in the definition of fuzzy preference structures. (I). General argumentation

1998 ◽  
Vol 97 (3) ◽  
pp. 349-359 ◽  
Author(s):  
Bartel Van de Walle ◽  
Bernard De Baets ◽  
Etienne Kerre
Keyword(s):  
Preference Structures ◽  
Definition Of ◽  
Fuzzy Preference

Maxitive Fuzzy Preference Structures

2000 ◽  
pp. 355-363 ◽  
Author(s):  
Bernard Baets ◽  
János Fodor
Keyword(s):  
Preference Structures ◽  
Fuzzy Preference

scholarly journals Introduction to Formal Preference Spaces

2013 ◽  
Vol 21 (3) ◽  
pp. 223-233
Author(s):  
Eliza Niewiadomska ◽  
Adam Grabowski
Keyword(s):  
Binary Relation ◽  
Preference Relation ◽  
Consumer Preference ◽  
Consumer Theory ◽  
Mathematical Economics ◽  
Characteristic Relation ◽  
Finite Set ◽  
Preference Structures ◽  
Equal Interest

Summary In the article the formal characterization of preference spaces [1] is given. As the preference relation is one of the very basic notions of mathematical economics [9], it prepares some ground for a more thorough formalization of consumer theory (although some work has already been done - see [17]). There was an attempt to formalize similar results in Mizar, but this work seems still unfinished [18]. There are many approaches to preferences in literature. We modelled them in a rather illustrative way (similar structures were considered in [8]): either the consumer (strictly) prefers an alternative, or they are of equal interest; he/she could also have no opinion of the choice. Then our structures are based on three relations on the (arbitrary, not necessarily finite) set of alternatives. The completeness property can however also be modelled, although we rather follow [2] which is more general [12]. Additionally we assume all three relations are disjoint and their set-theoretic union gives a whole universe of alternatives. We constructed some positive and negative examples of preference structures; the main aim of the article however is to give the characterization of consumer preference structures in terms of a binary relation, called characteristic relation [10], and to show the way the corresponding structure can be obtained only using this relation. Finally, we show the connection between tournament and total spaces and usual properties of the ordering relations.

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