Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems

Abstract

An iterative technique based on the use of parametric functions is proposed in this paper to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem (MOLFPP). Each fractional objective is transformed into a non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively calculated and the intuitionistic fuzzy optimization method is used to solve a multi-objective linear programming problem. Also, some basic properties and operations of an intuitionistic fuzzy set are considered. The development of the proposed algorithm is based on the principle of optimal decision set achieved by the intersection of various intuitionistic fuzzy decision sets which are obtained corresponding to each objective function. Additionally, as the intuitionistic fuzzy optimization method utilizes the degree of belonging and degree of non-belonging, we used the linear membership function for belonging and non-belonging to see its impact on optimization and to get insight into such an optimization process. The proposed approaches have been illustrated with numerical examples.