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Representations of a Comparison Measure Between Two Fuzzy Sets
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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.
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
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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