On fuzzy methodology to solve multi-objective linear optimization problem in fully intuitionistic fuzzy environment
TL;DR
A solution methodology is developed which utilizes the concepts of weighting sum approach, centroid of fuzzy numbers and component wise optimization to equivalently derive a deterministic multi-objective linear optimization.
Abstract
Optimization problems comprising multiple conflicting objectives and uncertain parameters, are often encountered in numerous practical fields. This paper studies the multi-objective linear optimization problems in a fully fuzzy environment comprising all its parameters including decision variables in the form of triangular intuitionistic fuzzy numbers which deals with both degrees of membership and non-membership. A solution methodology is developed which utilizes the concepts of weighting sum approach, centroid of fuzzy numbers and component wise optimization to equivalently derive a deterministic multi-objective linear optimization. Further, two different approaches are used to generate various sets of fuzzy Pareto optimal solutions. The concepts of linear, nonlinear membership functions (parabolic, hyperbolic, exponential) and $\epsilon$-constraint method are utilized in approach-I and II respectively to derive different sets of solutions. For illustration and validation purposes, an existing numerical problem is solved. The computational results are comparatively discussed which signifies the advantages, feasibility and acceptability of the proposed methodology.