Affiliations: [a] Department of Mathematics, Government College of Engineering and Textile Technology, Serampore, India | [b] Department of Mathematics, Bhairab Ganguly College, Kolkata, India | [c] Department of Mathematics, University of Kalyani, Kalyani, India
Correspondence:
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Corresponding author: Animeah Biswas, Department of Mathematics, University of Kalyani, Kalyani 741235, India. E-mail: abiswaskln@rediffmail.com.
Abstract: A new technique for solving fuzzy multiobjective chance constrained programming problems associated with Cauchy distributed and extreme value distributed fuzzy random variables is developed in this paper. The proposed methodology includes both fuzziness and randomness under one roof. At first fuzzy programming model is constructed from the fuzzy probabilistic model applying chance constrained programming methodology and α-cuts. Then using the method of defuzzification with probability density function of the corresponding membership functions the fuzzy model is converted into the deterministic one. Afterward by setting the imprecise aspiration level for each of the individual objectives, the membership functions are defined to measure the degree of achievements of the goal levels of the objectives. Finally, a weighted fuzzy goal programming technique is applied to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing under deviational variables in the decision making context. To illustrate the proposed approach, a practical application is considered and solved and then the achieved solution is compared with the other existing technique.
Keywords: Chance constrained programming, Cauchy distribution, defuzzification, extreme value distribution, fuzzy goal programming, fuzzy random variable, multiobjective programming
