Working Paper Article Version 1 This version is not peer-reviewed

# Representations of a Comparison Measure Between Two Fuzzy Sets

Version 1 : Received: 24 October 2020 / Approved: 26 October 2020 / Online: 26 October 2020 (14:16:55 CET)

A peer-reviewed article of this Preprint also exists.

Chen, J.-H.; Tang, H.-C. Representations of a Comparison Measure between Two Fuzzy Sets. Symmetry 2020, 12, 2008. Chen, J.-H.; Tang, H.-C. Representations of a Comparison Measure between Two Fuzzy Sets. Symmetry 2020, 12, 2008.

Journal reference: Symmetry 2020, 12, 2008
DOI: 10.3390/sym12122008

## Abstract

This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: the two disjoint union fuzzy sets, the two disjoint fuzzy sets and the two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for the two disjoint union fuzzy sets. There are 42 candidate representations of a comparison measure for the two disjoint fuzzy sets. Of which 13 candidate representations with one or two terms can be used to easily calculate and compare a comparison measure.

## Keywords

fuzzy set; comparison measure; representation; disjoint

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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