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Direct Product of Picture Fuzzy Subgroups

Taiwo O. Sangodapo

Abstract

In this paper, the concept of a picture fuzzy subgroup of a group is studied, and the notion of the direct product of picture fuzzy subgroups is introduced. Several characterisations of the direct product of picture fuzzy subgroups are established using the $(r, s, t)$-cut sets of picture fuzzy sets.

Direct Product of Picture Fuzzy Subgroups

Abstract

In this paper, the concept of a picture fuzzy subgroup of a group is studied, and the notion of the direct product of picture fuzzy subgroups is introduced. Several characterisations of the direct product of picture fuzzy subgroups are established using the -cut sets of picture fuzzy sets.
Paper Structure (3 sections, 12 theorems, 32 equations)

This paper contains 3 sections, 12 theorems, 32 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Direct Product of Picture Fuzzy Subgroups

Key Result

Theorem 2.1

dp Let $(G, \ast)$ be a crisp group and $Q = (\sigma_{Q}, \tau_Q, \eta_Q)$ be a PFSG of $G$. Then, $Q$ is a PFSG (PFNSG) if and only if $C_{r, s, t} (Q)$ is a crisp subgroup (normal) of $G$.

Theorems & Definitions (31)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Theorem 2.1
  • Definition 2.6
  • Definition 2.7
  • Definition 2.8
  • Proposition 2.1
  • ...and 21 more