Solving the fully fuzzy multi-choice linear programming model

Abstract

Purpose: Fuzzy multi-choice problems are widely used in the real world in the fields of industry, agriculture, science, technology, etc. Therefore, studying and solving such problems is essential. This study introduces some methods to solve fully fuzzy multi-choice linear programming problems.Methodology: To solve the fully fuzzy multi-choice linear programming problems, we use the linear least squares polynomial to convert the multi-choice linear programming problem to a mixed integer linear programming problem. Also, we convert the problem from the fuzzy mode to the crisp mode by using the defuzzification methods (Roubens ranking function.Findings: To investigate the efficiency of the suggested method, we solve and compare two fully fuzzy multi-choice linear programming models using the proposed methods. In general, the resulting algorithms are simple and very inexpensive to implement, and they are more efficient than those of previous studies.Originality/Value: In this article, all parameters and coefficients of the problem are triangular fuzzy numbers, and the right side of the problem's constraints are the fuzzy multi-choice parameters. The number of fuzzy multi-choice parameters in the previous articles has been considered only two fuzzy choices. However, in this article, the number of these parameters can be arbitrary. Also, this article uses the fuzzy linear least squares method to approximate the fuzzy multi-choice parameters.

Keywords

• fuzzy multi-choice programming
• fuzzy linear least squares method
• mixed integer linear programming problem
• defuzzification
• ranking function