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

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.

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

Multi-Objective Optimization , Fully fuzzy programming , Triangular fuzzy numbers , Interval valued functions , Weighting sum approach