Alternative Determines Positivity of Hexagonal Fuzzy Numbers and Their Alternative Arithmetic

Susmitha Harun,Sri Gemawati,Mashadi Mashadi

doi:10.11648/j.ijmfs.20200601.11

Abstract

There are quite a lot of arithmetic operations for hexagonal fuzzy numbers, most of them only define positive fuzzy numbers and few are discussing negative fuzzy numbers. And rarely found inverse of a fuzzy hexagonal number. So, often the results obtained in a hexagonal fuzzy linear equation system are not compatible. In this paper, we will discuss arithmetic alternatives on fuzzy hexagonal numbers. In this paper will definitions of positive and negative fuzzy numbers based on the concept of wide area covered by hexagonal fuzzy numbers in quadrant I and in quadrant II (right and left segments called r). From the concept of positivity and negativity the hexagonal fuzzy numbers will be constructed arithmetic alternatives for hexagonal fuzzy numbers. At the final part be given an inverse for a hexagonal fuzzy number so that, so for any fuzzy number there is an inverse hexagonal fuzzy number and its multiplication produces an identity.

Highlights

Fuzzy logic is part of mathematics science introduced by L.A Zadeh in 1965 [8, 9]
One that often appears in various forms of arithmetic for hexagonal fuzzy numbers is for any hexagonal fuzzy number not necessarily be valid
Based on the conditions above, the author feels the need to define the concept of positivity of a fuzzy hexagonal number by using the difference in the concept of wide area in quadrant I with quadrant II and the arithmetic alternative will be constructed for fuzzy hexagonal numbers with convex

Summary

Introduction

Fuzzy logic is part of mathematics science introduced by L. In [13] a positive fuzzy number is defined, if. 0, for all 1, 2, 3, 4, 5, 6 and the opposite is said negative this condition does not answer for fuzzy hexagonal numbers contain 0. While the study [11] discusses in the α-cut form but the hexagon fuzzy number form does not convex and the conditions mentioned above do not apply. Based on the conditions above, the author feels the need to define the concept of positivity of a fuzzy hexagonal number by using the difference in the concept of wide area in quadrant I with quadrant II (the difference between the area to the right of the r axis and the area to the left of the r axis) and the arithmetic alternative will be constructed for fuzzy hexagonal numbers with convex. The author will define hexagonal fuzzy numbers in the form. Susmitha Harun et al.: Alternative Determines Positivity of Hexagonal Fuzzy Numbers and Their Alternative Arithmetic

Preliminaries

Positive Fuzzy and Negative Fuzzy Numbers

New Arithmetic Hexagonal Fuzzy Number

Conclusion