Extended Equivalence of Fuzzy Sets
Venkat Murali, Sithembele Nkonkobe
TL;DR
This paper introduces a refined version of preferential equality for fuzzy sets, derives combinatorial formulas for counting such fuzzy subsets, and explores their asymptotic behavior.
Contribution
It presents a new tightened form of preferential equality for fuzzy sets and provides combinatorial and asymptotic analyses for these fuzzy subsets.
Findings
Derived combinatorial formulas for tight fuzzy subsets
Established asymptotic properties of fuzzy subset counts
Extended classical set equality concepts to fuzzy set theory
Abstract
Preferential equality is an equivalence relation on fuzzy subsets of finite sets and is a generalization of classical equality of subsets. In this paper we introduce a tightened version of the preferential equality on fuzzy subsets and derive some important combinatorial formulae for the number of such tight fuzzy subsets of an n-element set where n is a natural number. We also offer some asymptotic results
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Taxonomy
TopicsFuzzy Logic and Control Systems