On fuzzy tournaments and their solution concepts in group decision making
European Journal of Operational ResearchPublished 1 March 1991
Hannu Nurmi, Janusz Kacprzyk
Citations72
SJR quartileQ1
SJR score2.24
SNIP2.62
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
These new solution concepts are mainly counterparts of some sets of undominated options, uncovered sets, and Banks sets in group decision making as counterparts of the respective solution concepts in the case of nonfuzzy tournaments.
Abstract
Assuming as the point of departure a set of individual or collective fuzzy tournaments (complete and reciprocal binary relations)—representing the preferences of the particular individuals or their group as a whole, respectively—we define some new solution concepts in group decision making as counterparts of the respective solution concepts in the case of nonfuzzy tournaments (complete and asymmetric binary relations). Basically, the new solution concepts are mainly counterparts of some sets of undominated options, uncovered sets, and Banks sets. We consider the cases of both the conventional (nonfuzzy) and fuzzy majorities.
Keywords
Computer ScienceDecision SciencesMathematics
Fuzzy Set Theory—and Its Applications
7,484 Citations2001H.-J. Zimmermann
Computers & Mathematics with ApplicationsA computational approach to fuzzy quantifiers in natural languages
1,825 Citations1983Lotfi A. Zadeh
Fuzzy Sets, Decision Making, and Expert Systems
1,491 Citations1987H.-J. Zimmermann
This book discusses the Logic of Decisions, Behavioral Decision Theory, and Decision Technology, as well as an Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.
Fuzzy Sets and SystemsFuzzy preference orderings in group decision making
1,163 Citations1984Tetsuzo Tanino
F fuzzy preference orderings are defined as fuzzy binary relations satisfying reciprocity and max-min transitivity and those orderings might be useful for proceeding the group decision making process smoothly, in the same manner as the extended contributive rule method.
Fuzzy Sets and SystemsGroup decision making with a fuzzy linguistic majority
690 Citations1986Janusz Kacprzyk
Using the fuzzy majority rule specified by a fuzzy linguistic quantifier, a calculus of linguistically quantified propositions is applied and various solution concepts are derived, mainly of the type of core, minimax (opposition) set and consensus winner.
SIAM Journal on Applied MathematicsCondorcet Social Choice Functions
557 Citations1977Peter C. Fishburn
American Journal of Political ScienceA New Solution Set for Tournaments and Majority Voting: Further Graph- Theoretical Approaches to the Theory of Voting
488 Citations1980Nicholas R. Miller
European Journal of Operational ResearchA ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences
438 Citations1988Janusz Kacprzyk, Mario Fedrizzi
A new measure (degree) of consensus is proposed which is more human-consistent in the sense that it better reflects a real human perception of the essence of consensus in practice.
Fuzzy Sets and SystemsApproaches to collective decision making with fuzzy preference relations
356 Citations1981Hannu Nurmi
It turns out that some of the new solution concepts derived from the collective decision making theory are subsets of their nonfuzzy counterparts as subsets.
Social Choice and WelfareSophisticated voting outcomes and agenda control
292 Citations1985Jeffrey S. Banks
The uncovered set, as first defined by Miller (1980), is shown to be potentially reducible, and conditions are determined for which this reduction equals the set of sophisticated voting outcomes.
Kodo Keiryogaku (The Japanese Journal of Behaviormetrics)FUZZY SET THEORY AND ITS APPLICATIONS
289 Citations1986Nakaji Honda, Ario Ohsato
F fuzzy set theory which provides a methodology of treating human subjectivity, linguistic meanings, etc. is reviewed and its novel applications to some actual problems are introduced to show the efficiency of the theory.
Comparing Voting Systems
280 Citations1987Hannu Nurmi
Fuzzy Sets and SystemsA fuzzy relation space for group decision theory
272 Citations1978James C. Bezdek, Bonnie Spillman +1 more
Rec reciprocal relations over n alternatives are defined, and their efficacy as a model of the group decision process is investigated, and an application of this model for assessing degree of consensus is given.
Lecture notes in economics and mathematical systemsFuzzy Preference Relations in Group Decision Making
228 Citations1988Tetsuzo Tanino
This paper surveys how fuzzy preference relations are utilized in group decision making and proposes a systems analytic approach which aims to generate a practically meaningful group fuzzy preference relation which reflects differences or diversity of individual preferences.
Journal of CyberneticsFuzzy Relations in Group Decision Theory
163 Citations1974Jean-Marie Blin
An algorithm to map fuzzy orderings on non-fuzzy ones is proposed to guide the decision-maker in reaching decisions which reflect the fuzziness of the preferences over the available options.
American Journal of Political ScienceGraph-Theoretical Approaches to the Theory of Voting
152 Citations1977Nicholas R. Miller
British Journal of Political ScienceVoting Procedures: A Summary Analysis
145 Citations1983Hannu Nurmi
Journal of CyberneticsFuzzy Sets and Social Choice
131 Citations1973Jean M. Blin†, Andrew B. Whinston
Fuzzy Sets and SystemsFuzzy relation spaces for group decision theory: An application
98 Citations1979James C. Bezdek, Bonnie Spillman +1 more
One possible application of a fuzzy relation-theoretic model for group decision theory is exemplified; references to other published applications and closely related work are updated; and suggestions for potential research along several lines of theory and applications are expanded.
Systems Research and Behavioral ScienceA comparative analysis of social choice functions, IV
78 Citations1981Jeffrey T. Richelson
A Fuzzy Analysis of Consensus in Small Groups
77 Citations1980Bonnie Spillman, Richard Spillman +1 more
A new measure of consensus in small groups based on fuzzy mathematics which overcomes the difficulties found in other fuzzy consensus measures is examined, useful in analyzing how groups reach a decision.
Fuzzy Sets and SystemsSome problems on the definition of fuzzy preference relations
46 Citations1986Javier Montero, Juan Tejada
This paper proposes the problem of finding a max-min transitive relation as near as possible to a given initial preference relation, under the least-squares criterion and such that it does not introduce deep qualitative changes.
Lecture notes in economics and mathematical systemsOn Measuring Consensus in the Setting of Fuzzy Preference Relations
46 Citations1988Mario Fedrizzi, Janusz Kacprzyk
A ‘soft’ consensus measure which is basically a degree to which most pairs of individuals agree as to their preferences between almost all relevant options, and the point of departure is the set of individual preference relations.
Fuzzy Sets and SystemsDesign of group decisions II. In spaces of partial order fuzzy relations
31 Citations1980V.B. Kuz'min, С. В. Овчинников
Fuzzy Sets and SystemsGroup decisions I. In arbitrary spaces of fuzzy binary relations
28 Citations1980V.B. Kuz'min, С. В. Овчинников
The solution to the problem of finding a set of group decisions that satisfy the classical Pareto unanimity principle for the case of initial data represented as fuzzy relations of individual preference is solved.
Fuzzy measures of preference and consensus in group decision-making
24 Citations1977James C. Bezdek, Bonnie Spillman +1 more
A flat, convex set of fuzzy relations is utilizes to provide a physically realistic and mathematically tractable model for small group decision theory.
Lecture notes in economics and mathematical systemsAssumptions of Individual Preferences in the Theory of Voting Procedures
17 Citations1988Hannu Nurmi
Cybernetics & SystemsKINETIC THEORY OF “HOT” NEURAL SYSTEMS
5 Citations1987Francesco Ventriglia
The kinetic theory of neural systems is modified in order to allow the description of systems, such as the cerebral cortex, with a mixing of short range random connections and long range deterministic connections.