TAILIEUCHUNG - Linear programming problems with some multi-choice fuzzy parameters

In this paper, we consider some Multi-choice linear programming (MCLP) problems where the alternative values of the multi-choice parameters are fuzzy numbers. There are some real-life situations where we need to choose a value for a parameter from a set of different choices to optimize our objective, and those values of the parameters can be imprecise or fuzzy. We formulate these situations as a mathematical model by using some fuzzy numbers for the alternatives. | Yugoslav Journal of Operations Research 28 (2018), Number 2, 249–264 DOI: LINEAR PROGRAMMING PROBLEMS WITH SOME MULTI-CHOICE FUZZY PARAMETERS Avik PRADHAN Department of Mathematics, Indian Institute of Technology Kharagpur avik02iitkgp@ Mahendra PRASAD BISWAL Faculty of Department of Mathematics, Indian Institute of Technology Kharagpur mpbiswal@ Received: May 2016 / Accepted: November 2017 Abstract: In this paper, we consider some Multi-choice linear programming (MCLP) problems where the alternative values of the multi-choice parameters are fuzzy numbers. There are some real-life situations where we need to choose a value for a parameter from a set of different choices to optimize our objective, and those values of the parameters can be imprecise or fuzzy. We formulate these situations as a mathematical model by using some fuzzy numbers for the alternatives. A defuzzification method based on incentre point of a triangle has been used to find the defuzzified values of the fuzzy numbers. We determine an equivalent crisp multi-choice linear programming model. To tackle the multi-choice parameters, we use Lagranges interpolating polynomials. Then, we establish a transformed mixed integer nonlinear programming problem. By solving the transformed non-linear programming model, we obtain the optimal solution for the original problem. Finally, two numerical examples are presented to demonstrate the proposed model and methodology. Keywords: Linear Programming, Triangular Fuzzy Number, Trapezoidal Fuzzy Number, Multi-choice Programming, Fuzzy Programming. MSC: 90C05, 90C11, 90C70. 1. INTRODUCTION In real life decision making situations, we face several types of optimization problems. The articles related to both optimization methods and models can be found very frequently in the literature of optimization. Every new real-life 250 A. Pradhan, . Biswal / LPP with MCF Parameter decision-making .

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