Arithmetic Modifications of Pentagonal Fuzzy Numbers and G-Inverse Applications
Era Napra Tilopa, Mashadi, Sri Gemawati

University of Riau

Abstract

Pentagonal fuzzy numbers are an extension of triangular fuzzy numbers. This paper presents various alternatives for the arithmetic operations of pentagonal fuzzy numbers, including addition, subtraction, scalar multiplication, multiplication, division, and inversion. Some researchers have defined the inverse of pentagonal fuzzy numbers in parametric form. However, this approach does not always result in a x a inverse is an identity. which affects the process of determining the inverse of pentagonal fuzzy number matrices. In this paper, the author has introduced new arithmetic modifications for the multiplication, division, and inversion of pentagonal fuzzy numbers. The modified arithmetic results have been used to determine the inverse of pentagonal fuzzy matrices. Additionally, new arithmetic modifications have been developed to determine the G-Inverse for any m x n pentagonal fuzzy matrix or singular matrix. Thus, the application of pentagonal fuzzy numbers using inversion and G-Inverse can produce appropriate solutions.

Keywords: Fuzzy numbers, Arithmetic of fuzzy numbers, Inverse of pentagonal fuzzy number matrices, G-Inverse.

Topic: Mathematics