A Computational Method for Fuzzy Arithmetic Operations on Bipolar Fuzzy Numbers and Its Application

Subject Areas : Statistics

Fazlollah  Abbasi ¹ (Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran)
sahleh  shakeri ² (Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University,Amol, Iran)

Received: 2019-10-26 Accepted : 2020-01-14 Published : 2021-09-23

Keywords: اعداد فازی دو قطبی, معادله خطی فازی دو قطبی, حساب فازی دو قطبی, اعمال انتقال-میانگین,

Abstract :

A bipolar fuzzy set is a powerful tool for depicting fuzziness and uncertainty. This model is more flexible and practical as compared to the fuzzy model. We define certain notions, including a bipolar fuzzy number and bipolar fuzzy arithmetic. In this paper we propose the new fuzzy arithmetic operations based on on bipolar fuzzy numbers from [1,2]. We define 2- dipole fuzzy numbers and cutting them. The properties of these propose operations and their fundamental qualities are discussed in detail. Several illustrative examples were given to show the accomplishment and ability of the proposed method. At the end it is shown that the solution of the proposed method in comparison to other methods of solving fuzzy equations are more realistic, that is, they have smaller support. Further, we analyze our new approach to find the solutions of a bipolar fuzzy linear equations. In this paper, in addition to familiarity with bipolar fuzzy number operations based on transmission- average and presenting practical solutions for calculations in specific cases, this problem is identified.

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