Two New Intuitionistic Fuzzy Interactive Methods For Multilevel Programming

Multilevel programming problem is a kind of mathematical programming problem with nested hierarchical structure,which is widely used in agriculture,industry,finance,transportation,government strategy,cloud computing pricing,supply chain management and other fields.This kind of problem is NP-hard non-convex and non-smooth optimization problem.The complexity of its solution increases with the increase of the scale and level of the problem.Therefore,it is of great practical significance and application value to apply the theory of fuzzy sets and intuitionistic fuzzy sets to solve multi-level programming problems in order to find satisfactory solutions that can meet the requirements of decision makers as much as possible.This paper mainly studies the decision-making methods for solving multi-level programming problems,so as to find a satisfactory solution strategy for each decision-maker.Because decision-makers have different preferences for decision-making in practical problems,intuitionistic fuzzy interactive methods based on parabolic,hyperbolic membership function and non-membership function are proposed respectively.Firstly,parabolic and hyperbolic membership function are given.Secondly,in order to increase the objectivity of decision-making,a new score function is constructed to describe the satisfaction degree of decision-makers.The values of fuzzy parameters in the score function are selected according to the different personalized choices of decision-makers,and the decision-making is distinguished based on the different preferences of decision-makers to satisfaction.Thirdly,the decision-making is distinguished by combining minimax method and utility function.Finally,numerical experiments show that the method is feasible and effective.