Entropy, distance measure and similarity measure of fuzzy sets and their relations

Fuzzy Sets and SystemsPublished 1 December 1992

Xuecheng Liu

DOI10.1016/0165-0114(92)90239-z

Source URL

Citations572

SJR quartileQ1

SJR score0.75

SNIP1.25

TL;DR

The axiom definitions of entropy, distance measure and similarity measure of fuzzy sets are systematically given and basic relations between these measures are discussed.

Abstract

The axiom definitions of entropy, distance measure and similarity measure of fuzzy sets are systematically given and basic relations between these measures are discussed. The concepts of σ- (resp. sub-σ-)entropy, σ- (resp. sub-σ-)distance measure and σ- (resp. sub-σ-)similarity measure are proposed, and some examples of them are listed. The relations between σ- (resp. sub-σ-)entropy, σ- (resp. sub-σ-)distance measure and σ- (resp. sub-σ-)similarity measure are obtained.

Keywords

Computer ScienceDecision SciencesMathematics

Information and ControlFuzzy sets

66,132 Citations1965L. A. Zadeh

Fuzzy Set Theory—and Its Applications

7,484 Citations2001H.-J. Zimmermann

Information and ControlA definition of a nonprobabilistic entropy in the setting of fuzzy sets theory

2,260 Citations1972Aldo de Luca, S. Termini

A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.

International Journal of General SystemsON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval

579 Citations1979Ronald R. Yager

It is suggested that fuzziness can be related to the lack of distinction between a set and its negation and the concept of compatibility is used to develop linguistic measures of fuzziness.

Medical Entomology and ZoologyFuzzy Mathematical Approach to Pattern Recognition

512 Citations1986Sankar K. Pal, Dwijesh K. Dutta-Majumder

Results of investigations, both experimental and theoretical, are presented into the effectiveness of fuzzy algorithms as classification tools in some problems concerned with the field of pattern recognition and image processing.

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.

View PDF

Fuzzy Sets and SystemsWhere do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?

181 Citations1987George J. Klir

It is argued in this paper that each of the four types of uncertainty measures can be used for measuring structural (syntactic) information in the same sense as the Hartley and Shannon measures have been used in this respect.

International Journal of General SystemsON MEASURES OF FUZZINESS AND FUZZY COMPLEMENTS

139 Citations1982Masahiko Higashi, George J. Klir

An axiomatic framework for formalizing the most general class of fuzzy complements is introduced and it is shown that the various measures of fuzziness described previously in the literature are special cases of this general class.