A Modal Account of Preference in a Fuzzy Setting

Autoři: Amanda Vidal Wandelmer, Ph.D.
Rok vydání: 2018
Typ publikace: Kapitola v monografii
Periodikum: Soft Computing Based Optimization and Decision Models
Projekty: Modelování vágních kvantifikátorů v matematické fuzzy logice
Bibliografická citace: ESTEVA, F., GODO, L., VIDAL, Amanda. A Modal Account of Preference in a Fuzzy Setting. In: PELTA, D.A., CORONA, C.C., eds. Soft Computing Based Optimization and Decision Models. Cham: Springer, 2018, S. 241-260. Studies in Fuzziness and Soft Computing, 360. ISBN 978-3-319-64285-7
Dostupné z: doi:10.1007/978-3-319-64286-4_15.
DOI: 10.1007/978-3-319-64286-4_15
ID: 478661
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Abstrakt

In this paper we first consider the problem of extending fuzzy (weak and strict) preference relations, represented by fuzzy preorders on a set to a fuzzy preferences on subsets, and we characterise different possibilities. Based on their properties, we then semantically define and axiomatize several two-tiered graded modal logics to reason about the corresponding different notions of fuzzy preferences. This paper is our humble contribution to the tribute, in the occasion of his 65th birthday, to José Luis “Curro” Verdegay. Excellent researcher and better person, he has been one of the pioneers of fuzzy logic in Spain and founder and driving force of the research group on Decision Making and Optimization at the University of Granada. Our contribution is devoted to logic and fuzzy preferences, a topic that, although it is not central on the research of Curro, is ubiquitous in fuzzy decision making models and we hope it may be of his interest. Along many years, we have jointly participated in many events around the world with Curro and with our friends from Granada, we have learnt a lot from his research ideas and organizational competences, but more importantly, we have enjoyed his friendship and shared many unforgettable moments. Thanks for all Curro, and congratulations for this well-deserved homage!