Pareto-optimal solution for fixed-charge solid transportation problem under intuitionistic fuzzy environment

Abstract An intuitionistic fuzzy transportation problem considers both membership as well as non-membership functions. It may be linear or non-linear. In the literature, a lot of work is done in the case of linear membership and non-membership functions, but not in non-linear functions. The presented paper defines the non-membership functions of hyperbolic and exponential functions. The novelty lies in suggesting a unique approach of obtaining pareto-optimal solution of multi-objective fixed-charge solid transportation problem by using intuitionistic fuzzy programming approach with linear, hyperbolic, and exponential membership as well as non-membership functions. A real-life numerical illustration is solved, which exhibits the suitability of the proposed methodology as well as the functionality of all the membership and non-membership functions considered here.

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