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Extended Equivalence of Fuzzy Sets

Venkat Murali, Sithembele Nkonkobe

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

Extended Equivalence of Fuzzy Sets

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

Paper Structure

This paper contains 3 sections, 3 theorems, 4 equations, 1 table.

Table of Contents

  1. Introduction
  2. Image, kernel and ordered partition
  3. THE EXTENDED EQUIVALENCE

Key Result

Theorem \oldthetheorem

For $n\geq 1$ and $k\geq1$:

Theorems & Definitions (7)

  • Definition 3.1: Tight-$\alpha$-cut
  • Theorem \oldthetheorem
  • proof
  • Theorem \oldthetheorem
  • proof
  • Theorem \oldthetheorem
  • proof