New Computational Technique for Solving Linear Programming Problem Subjected to Fuzzy Uncertainty

Dennis Xavier, Santhi Dennis Xavier and Diptiranjan Behera
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Dennis Xavier: School of Mathematics and Statistics, University of Technology, Jamaica 237 Old Hope Road Kingston 6, Jamaica, West Indies
Santhi Dennis Xavier: ��Department of Mathematics, The Mico University College, 1 Marescauex Road, Kingston 5 Jamaica, West Indies
Diptiranjan Behera: ��Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7 Jamaica, West Indies

New Mathematics and Natural Computation (NMNC), 2024, vol. 20, issue 01, 13-25

Abstract: This paper proposes two new computational methods for solving linear programming problem under trapezoidal and triangular fuzzy uncertainties with equality constraints. The coefficients of the constraints and the objective functions are assumed to be crisp. However, the decision variables and the right-hand side vector of the constraints are considered as uncertain in nature. The concepts of fuzzy addition and subtraction have been used to develop the proposed methods. In the first method, the coefficients are considered as non-negative, whereas mixed coefficients (i.e. both negative and non-negative) are considered in the second method. The obtained results are compared with Behera et al. [D. Behera, K. Peters and S. A. Edalatpanah, Alternative methods for linear programming problem under triangular fuzzy uncertainty, Journal of Statistics and Management Systems, 25 (2022) 521–539; D. Behera, K. Peters, S. A. Edalatpanah and D. Qiu, New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty, Journal of Information and Optimization Sciences, 42 (2021) 603–629], and Saati et al. [S. Saati, M. Tavana, A. Hatami-Marbini and E. Hajiakhondi, A fuzzy linear programming model with fuzzy parameters and decision variables, International Journal of Information and Decision Sciences, 7 (2015) 312–333.] for the validation.

Keywords: Fuzzy linear programming problem; fuzzy number; α-cut; fuzzy arithmetic (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S1793005724500029

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