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Fuzzy Set with Hyperbolic Valued Membership Function

Chinmay Ghosh, Sanjib Kumar Datta, Soumen Mondal

Abstract

In this article, we have introdued D-fuzzy sets. We have discussed the notions of inclusion, union, intersection, complementation and convexity of such D-fuzzy sets. Also we have proved separation theorem of convex D-fuzzy sets.

Fuzzy Set with Hyperbolic Valued Membership Function

Abstract

In this article, we have introdued D-fuzzy sets. We have discussed the notions of inclusion, union, intersection, complementation and convexity of such D-fuzzy sets. Also we have proved separation theorem of convex D-fuzzy sets.
Paper Structure (2 sections, 9 theorems, 58 equations)

This paper contains 2 sections, 9 theorems, 58 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Main Results

Key Result

Proposition 2

The union of two $\mathbb{D}$-fuzzy sets $A$ and $B$ is the smallest $\mathbb{D}$-fuzzy set containing $A$ and $B.$

Theorems & Definitions (15)

  • Example 1
  • Proposition 2
  • Proposition 3
  • Definition 4
  • Definition 5
  • Remark 6
  • Theorem 7
  • Theorem 8
  • Remark 9
  • Definition 10
  • ...and 5 more