scholarly journals Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 436 ◽  
Author(s):  
Armajac Raventós-Pujol ◽  
María J. Campión ◽  
Esteban Induráin
Keyword(s):  
Common Sense ◽  
New Technique ◽  
Impossibility Theorem ◽  
Binary Relations ◽  
Strict Preference ◽  
Weak Preference ◽  
Fuzzy Preferences ◽  
A New Technique ◽  
Fuzzy Setting ◽  
Fuzzy Preference

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

scholarly journals Representation and aggregation of crisp and fuzzy ordered structures: applications to social choice

2021 ◽  
Author(s):  
◽  
Armajac Raventós Pujol
Keyword(s):  
Social Choice ◽  
Impossibility Result ◽  
The Body ◽  
Main Body ◽  
Binary Relations ◽  
Open Problems ◽  
Weak Preference ◽  
Fuzzy Preferences ◽  
Fuzzy Aggregation ◽  
A New Technique

The present memory is structured as follows: after the Introduction, in the Chapter 2 of preliminaries, we will pay attention to the three areas which sustain the development of this thesis. These are, binary relations, Social Choice and Fuzzy sets. Chapter 3 is devoted to the study of fuzzy Arrovian models. First, it is introduced the concept of a fuzzy preference. Next, we define fuzzy aggregation rules and all of the restrictions of common sense, which are inspired by the restrictions that come from the classic Arrovian model. Next, different models are defined in the fuzzy setting. Their definitions depend on the particular nuances and features of a preference (choosing a transitivity type and a connectedness type) and the restrictions on an aggregation function (choosing an independence of irrelevant alternatives property,an unanimity property, etc). Different possibility and impossibility theorems have been proved depending on the set of definition and restrictions. In Chapter 4 it is studied the problem of the decomposition of fuzzy binary relations. There, it is defined clearly the problem of setting suitable decomposition rules. That is, we analyze how to obtain a strict preference and an indifference from the weak preference in a fuzzy approach. In this chapter, the existence and the uniqueness of certain kind of decomposition rules associated to fuzzy unions are characterized. In Chapter 5, the decomposition rules studied in Chapter 4 are used to achieve a new impossibility result. It is important to point out that in the proof of the main result in this chapter it is introduced a new technique. In this proof, fuzzy preferences are framed through an auxiliary tuple of five crisp binary relations, that we name a pseudofuzzy preference. An aggregation model à la Arrow of pseudofuzzy preferences is also studied,but the main result is about the aggregation of fuzzy preferences that come from decompositions.Chapters 3, 4 and 5 constitute the main body of this memory. Then a section of conclusions is included. It contains suggestions for further studies, open problems and several final comments. Finally, an Appendix has been added in order to give an account of the work done within these three years, that can not be included in the body of the present memory.

ARROW-TYPE RESULTS UNDER INTUITIONISTIC FUZZY PREFERENCES

2013 ◽  
Vol 09 (01) ◽  
pp. 97-123 ◽  
Author(s):  
GILBERT NJANPONG NANA ◽  
LOUIS AIME FONO
Keyword(s):  
Positive Result ◽  
Social Preferences ◽  
Impossibility Theorem ◽  
Arrow’S Impossibility Theorem ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Preferences ◽  
Arrow's Impossibility Theorem ◽  
Fuzzy Preference

Fono et al.11 characterized, for an intuitionistic fuzzy t-norm [Formula: see text], two properties of a given regular intuitionistic fuzzy strict component of a (T,S)-transitive intuitionistic fuzzy preference. In this paper, we examine these characterizations in the particular case where [Formula: see text]. We then use these (general and particular) results to obtain some intuitionistic fuzzy versions of Arrow's impossibility theorem. Therefore, by weakening a requirement to social preferences, we deduce a positive result, that is, we display an example of a non-dictatorial Intuitionistic Fuzzy Agregation Rule (IFAR) and, we establish an intuitionistic fuzzy version of Gibbard's oligarchy theorem.

scholarly journals FUZZY STRICT PREFERENCE RELATIONS COMPATIBLE WITH FUZZY ORDERINGS

2010 ◽  
Vol 18 (01) ◽  
pp. 13-24 ◽  
Author(s):  
BONIFACIO LLAMAZARES ◽  
BERNARD DE BAETS
Keyword(s):  
Equivalence Relation ◽  
Preference Relation ◽  
Strict Preference ◽  
Preference Modelling ◽  
Preference Relations ◽  
Weak Preference ◽  
Indifference Relation ◽  
Definition Of ◽  
Fuzzy Orderings ◽  
Fuzzy Preference

One of the most important issues in the field of fuzzy preference modelling is the construction of a fuzzy strict preference relation and a fuzzy indifference relation from a fuzzy weak preference relation. Here, we focus on a particular class of fuzzy weak preference relations, the so-called fuzzy orderings. The definition of a fuzzy ordering involves a fuzzy equivalence relation and, in this paper, the latter will be considered as the corresponding fuzzy indifference relation. We search for fuzzy strict preference relations compatible with a given fuzzy ordering and its fuzzy indifference relation. In many situations, depending on the t-norm and t-conorm used, this quest results in a unique fuzzy strict preference relation. Our aim is to characterize these fuzzy strict preference relations and to study their transitivity.

A new technique for the mapping of oxygen tension on the brain surface

2005 ◽  
Vol 25 (1_suppl) ◽  
pp. S543-S543
Author(s):  
Satoshi Kimura ◽  
Keigo Matsumoto ◽  
Yoshio Imahori ◽  
Katsuyoshi Mineura ◽  
Toshiyuki Itoh
Keyword(s):  
Oxygen Tension ◽  
New Technique ◽  
Brain Surface ◽  
A New Technique ◽  
The Brain
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