Group decision making and consensus under fuzzy preferences and fuzzy majority
type: Item
instance of: scholarly article
title: Group decision making and consensus under fuzzy preferences and fuzzy majority
zbMATH Open document ID: 0768.90003
DOI: 10.1016/0165-0114(92)90107-F
author: Janusz Kacprzyk
author: Mario Fedrizzi
author: Hannu Nurmi
published in: Fuzzy Sets and Systems
publication date: 1993-01-16T00:00:00Z
review text: The paper develops fuzzy set-based models for fundamental relations of strict preference, indifference, and incomparability. This generalization is aimed at preserving all classical properties found in preference modelling. Recall that in this theory the above binary relations are defined in a given family \(A\) of alternatives as follows: Strict preference: \(aPb\) iff \(aRb\) and not \(bRa\); Indifference: \(aIb\) iff \(aRb\) and \(bRa\); Incomparability: \(aJb\) iff not \(aRb\) and not \(bRa\), where \(R\) denotes a binary relation of weak preference, say \(aRb\) iff \(a\) is at least as good as \(b\). The main results pertain to an extension of the classical results by proposing fuzzy models for the above relations. It is proved that a ``reasonable'' generalization (preserving the properties found in the Boolean case) should be based upon Lukasiewicz-like De Morgan triples.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 91B08
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 91990
zbMATH Keywords: fuzzy set-based models
zbMATH Keywords: strict preference
zbMATH Keywords: indifference
zbMATH Keywords: incomparability
MaRDI profile type: Publication
cites work: New problems in the general choice theory
cites work: Q3798428
cites work: GROUP DECISION-MAKING WITH A FUZZY MAJORITY VIA LINGUISTIC QUANTIFIERS. PART II: A COMPETITIVE-LIKE POOLING
cites work: Group decision making with a fuzzy linguistic majority
cites work: Q3798435
cites work: Q3768429
cites work: Q3777753
cites work: A ``human-consistent'' degree of consensus based on fuzzy logic with linguistic quantifiers
cites work: Multiperson decision making models using fuzzy sets and possibility theory
cites work: Non-conventional preference relations in decision making
cites work: Q3343800
cites work: ``Softer'' optimization and control models via fuzzy linguistic quantifiers
cites work: Q3352832
cites work: Q3818119
cites work: Prospect Theory: An Analysis of Decision under Risk
cites work: "Expected Utility" Analysis without the Independence Axiom
cites work: Approaches to collective decision making with fuzzy preference relations
cites work: Q3669134
cites work: On fuzzy tournaments and their solution concepts in group decision making
cites work: An application of fuzzy subsets theory to the analysis of the consumer's spatial preferences
cites work: Producer's spatial equilibrium with a fuzzy constraint
cites work: Fuzzy mathematical models in economics
cites work: Quantifiers in the formulation of multiple objective decision functions
cites work: Quantified propositions in a linguistic logic
cites work: Aggregating evidence using quantified statements
cites work: A computational approach to fuzzy quantifiers in natural languages
cites work: Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions
full work available at URL: 0165-0114(92)90107-f
OpenAlex ID: W2005836461
description: scientific article; zbMATH DE number 91990