Solving intuitionistic fuzzy multi-objective linear programming problem and its application in supply chain management

The aim of this paper is solving an intuitionistic fuzzy multi-objective linear programming problem containing intuitionistic fuzzy parameters, intuitionistic fuzzy maximization/minimization, and intuitionistic fuzzy constraints. To do this, a linear ranking function is used to convert the intuitionistic fuzzy parameters to crisp ones first. Then, linear membership and non-membership functions are used to manipulate intuitionistic fuzzy maximization/minimization and intuitionistic fuzzy constraints. Then, a multi-objective optimization problem is formulated containing maximization of membership functions and minimization of non-membership functions. To solve this problem, the minimax and weighted sum methods are used. Then, the described procedure is summarized as an algorithm to solve the problem, and a numerical example is solved by the proposed method. Finally, to investigate the capability and performance of the model, a supplier selection problem, which is one of the important applications in supply chain management, is solved by the proposed algorithm.