Reduction methods of type-2 fuzzy variables and their applications to Stackelberg game

摘要

This paper is designed based on the mathematical models for bi-level programming in Stackelberg game under type-2 fuzzy environment. The parameters of the objective functions on both levels are considered as type-2 fuzzy numbers in the first case whereas the parameters of the objective functions and the constraints are chosen as type-2 fuzzy numbers in the second case. Critical value based reduction methods are applied to reduce type-2 fuzzy numbers to type-1 fuzzy numbers in the first case. After that, centroid method is used for completely defuzzifying type-2 fuzzy numbers. Besides this, the obtained results are compared with the help of LINGO iterative scheme and genetic algorithm. Coming to the second case, a chance constraint programming with the help of generalized credibility measure is utilized to convert the fuzzy problem to its equivalent crisp form. LINGO iterative scheme is used to solve the deterministic problem using fuzzy programming. The sensitivity analysis is shown to different credibility levels of right hand side of the constraints to find the value of objective function in each level. Finally, real-life based numerical problems are presented to show the performance of the proposed models and techniques. At last, conclusion about the findings and outlook are described.