A generalization of the representation theorem
Fuzzy Sets and SystemsPublished 1 November 1992
Dan A. Ralescu
Citations48
SJR quartileQ1
SJR score0.75
SNIP1.25
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
The representation theorem for fuzzy sets is generalized and necessary and sufficient conditions for a family of sets to represent a “permutation” of the levels of some fuzzy set are given.
Abstract
We generalize the representation theorem for fuzzy sets. More specifically, we give necessary and sufficient conditions for a family of sets to represent a "permutation" of the levels of some fuzzy set.
Keywords
Computer ScienceDecision SciencesMathematics
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,964 Citations1978Lotfi A. Zadeh
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,280 Citations1999Lotfi A. Zadeh
The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
Information SciencesSimilarity relations and fuzzy orderings
2,621 Citations1971Lotfi A. Zadeh
An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
Birkhäuser Basel eBooksApplications of Fuzzy Sets to Systems Analysis
732 Citations1975C.V. Negoita, Dan A. Ralescu
IEEE Transactions on Systems Man and CyberneticsApplications of fuzzy sets to systems analysis
567 Citations1977C.V. Negoita, Dan A. Ralescu +1 more
Fuzzy Sets and SystemsMeasurement of membership functions and their acquisition
275 Citations1991İ.B. Türkşen
European Journal of Operational ResearchFuzzy sets, probability and measurement
195 Citations1989Didier Dubois, Henri Prade
These works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory; conversely Zadeh's logical point of view on fuzzy sets suggests a set-theoretic perspective on uncertainty measures, that brings together numerical quantification and logic.
TechnometricsSimulation, Knowledge-Based Computing and Fuzzy Statistics
108 Citations1989J. Michael Hardin
Fuzzy Sets and SystemsAlgebraic fuzzy systems
43 Citations1991U. M. Swamy, Dhandapani Raju
A general theory of algebraic fuzzy systems is developed by introducing the notion of a fuzzy L -subset corresponding to a set L of subsets of a nonempty set X assuming truth values in a complete Brouwerian lattice.
TechnometricsSimulation, Knowledge-Based Computing and Fuzzy Statistics
43 Citations1989J. Michael Hardin, Constantin Virgil Negoiţă +1 more
Journal of Mathematical Analysis and ApplicationsThe structure of the norm system on fuzzy sets
7 Citations1987Zhang Wenxiu, Le Huiling
The norm system is defined which provides the general model to fuzzy sets and systems and the extended operation's properties of fuzzy sets on the complete lattice are considered.
