Solution of Fully Bipolar Fuzzy Linear Programming Models | Zendy

Muhammad Athar Mehmood | Zendy; Muhammad Akram | Zendy; Majed Alharbi | Zendy; Shahida Bashir | Zendy

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Solution of Fully Bipolar Fuzzy Linear Programming Models

Author(s) -

Muhammad Athar Mehmood,

Muhammad Akram,

Majed Alharbi,

Shahida Bashir

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/9961891

Subject(s) - fuzzy number , mathematics , fuzzy logic , mathematical optimization , vagueness , defuzzification , fuzzy set operations , linear programming , fuzzy set , computer science , artificial intelligence

The Yin-Yang bipolar fuzzy set is a powerful mathematical tool for depicting fuzziness and vagueness. We first extend the concept of crisp linear programming problem in a bipolar fuzzy environment based on bipolar fuzzy numbers. We first define arithmetic operations of unrestricted bipolar fuzzy numbers and multiplication of an unrestricted trapezoidal bipolar fuzzy number (TrBFN) with non-negative TrBFN. We then propose a method for solving fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints in which the coefficients are unrestricted triangular bipolar fuzzy numbers and decision variables are nonnegative triangular bipolar fuzzy numbers. Furthermore, we present a method for solving FBFLPPs with equality constraints in which the coefficients and decision variables are unrestricted TrBFNs. The FBFLPP is transformed into a crisp linear programming problem, and then, it is solved to achieve the exact bipolar fuzzy optimal solution. We illustrate the proposed methodologies with several numerical examples.

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