A fuzzy solution approach to multi-objective fully triangular fuzzy optimization problem

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 مرداد 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.87836.1434

نویسندگان

Neelam Swain؛ Sujit Maharana؛ Suvasis Nayak^*

Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar, 751024, Odisha, India.

چکیده

Numerous optimization problems comprise uncertain data in practical circumstances and such uncertainty can be suitably addressed using the concept of fuzzy logic. This paper proposes a computationally efficient solution methodology to generate a set of fuzzy non-dominated solutions of a fully fuzzy multi-objective linear programming problem which incorporates all its parameters and decision variables expressed in the form of triangular fuzzy numbers. The fuzzy parameters associated with the objective functions are transformed into interval forms by utilizing the fuzzy cuts which subsequently generate the equivalent interval-valued objective functions and the concept of the centroid of triangular fuzzy numbers derives the deterministic form of the constraints.
Furthermore, the scalarization process of the weighting sum approach and certain concepts of interval analysis are used to generate the fuzzy non-dominated solutions from which the compromise solution can be determined based on the corresponding real-valued expressions of fuzzy optimal objective values resulting due to the ranking function. Three numerical and one practical problem are solved for illustration and validation of the proposed approach. The computational results are also discussed as compared to some existing methods.

کلیدواژه‌ها

Multi-objective optimization؛ Fully fuzzy programming؛ Triangular fuzzy numbers؛ Interval valued functions؛ Weighting sum approach