On solving chance constrained programming problems involving uniform distribution with fuzzy parameters

Article type: Research Article

Authors: Biswas, Animesh^{; *} | Modak, Nilkanta

Affiliations: Department of Mathematics, University of Kalyani, Kalyani, India

Correspondence: [*] Corresponding author: Animesh Biswas, Department of Mathematics, University of Kalyani, Kalyani 741235, India. Tel.: +91 3325828750; Fax: +91 3325828282; E-mail: [email protected].

Abstract: As a special field of mathematical programming, fuzzy chance constrained programming is now emerging as a promising area of study from the view point of its ability to capture fuzziness and randomness simultaneously. In this paper a fuzzy goal programming method has been presented for solving multiobjective chance constrained programming problems in which the right sided parameters associated with the system constraints are uniformly distributed fuzzy random variables. In the proposed approach the fuzzy chance constrained programming problem is converted first into its equivalent fuzzy programming form by using the concept of α-cuts. Then the problem is decomposed on the basis of tolerance ranges of fuzzy parameters associated with the system constraints. Next by setting imprecise aspiration level to each of the individual objectives, the membership function is defined to measure the degree of achievements of goal levels of the objectives. Afterwards a fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the group regrets consisting of under deviational variables of the fuzzy goals in the decision making context. To explore the potentiality of the proposed approach, an illustrative example is solved and the solution is compared with other technique.

Keywords: Multiobjective programming, chance constrained programming, uniform distribution, fuzzy numbers, fuzzy random variables, fuzzy goal programming

DOI: 10.3233/IDT-130158

Journal: Intelligent Decision Technologies, vol. 7, no. 2, pp. 151-159, 2013