Title: A fuzzy goal programming technique for multi-objective chance constrained programming with normally distributed fuzzy random variables and fuzzy numbers

Authors: Animesh Biswas; Nilkanta Modak

Addresses: Department of Mathematics, University of Kalyani, Kalyani – 741235, India ' Department of Mathematics, University of Kalyani, Kalyani – 741235, India

Abstract: This paper presents a fuzzy goal programming approach for modelling and solving multi-objective decision making problems having fuzzy random variables and fuzzy numbers associated with the system constraints. In the model formulation process, the problem is converted into an equivalent fuzzy programming problem by using chance constrained programming technique. The problem is then decomposed into sub problems by considering the tolerance limits of fuzzy numbers relating to the system constraints. The individual optimal solution of each objective is found to construct the membership goals. A two-phase fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership goals of the objectives to the extent possible by minimising under deviational variables and thereby obtaining most satisfactory solution in the decision making environment. A numerical example is solved to illustrate the proposed approach and the achieved solutions are compared with other existing methodologies.

Keywords: multi-objective programming; chance constrained programming; CCP; fuzzy numbers; fuzzy random variables; fuzzy programming; fuzzy goal programming; FGP; fuzzy logic; modelling; multi-objective decision making.

DOI: 10.1504/IJMOR.2013.056116

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.5, pp.551 - 570

Received: 08 Feb 2012
Accepted: 24 Jul 2012
Published online: 31 Mar 2014 *

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