The Research On Intuitionistic Fuzzy Numbers And Fuzzy Quadratic Programming

This paper puts forward a new solution which is called the tolerance method combined with penalty function method so as to solve fuzzy quadratic programming problem. First, the tolerance method is utilized to clarify fuzzy problems,then the penalty function method is adopted to solve the problems in question. At last, a numerical example is used to verify the feasibility of this method. Meanwhile, on the basis of intuitionistic fuzzy sets, the description of fuzzy quadratic programming problem constraints is realized by way of intuitionistic fuzzy number.In addition, the trapezoidal intuitionistic fuzzy numbers and triangle intuitionistic fuzzy numbers fuzzy programming problem are also studied. The results obtained further enriches the fuzzy set theory, providing a more accurate result for policymakers to solve uncertain problems.This paper includes four chapters. the first chapter is the introduction which is divided into two sections. The first section briefly introduces the selected topic background, significance and the development trend of the fuzzy quadratic programming, the second section mainly introduces the research content and the structure of the thesis in this paper.The second chapter is preliminary knowledge. First of all, the paper introduces the basic concept and basic properties of intuitionistic fuzzy sets, then moves to the concept of intuitionistic fuzzy number, which gives the basic concept, nature and operation rule of trapezoidal intuitionistic fuzzy numbers and triangle intuitionistic fuzzy numbers. This provides theoretical basis for the study.The third chapter mainly introduces several kinds of intuitionistic fuzzy number ranking method: weighted expectation, the value of the related fuzzy number and fuzzy degree method, the Hamming distance method. At the same time, it briefly explains these methods, which offers reference for solving the fuzzy quadratic programming problem contained with the intuitionistic fuzzy coefficient in the fifth chapter.The fourth chapter, which is the main content of this article, is about the content of fuzzy quadratic programming. First, it introduces classification of the fuzzy quadratic programming problem, and then explains the basic methods of solving fuzzy quadratic programming)tolerance method combined with penalty function method and ?-cut set method, which is a new kind of method. Further more, numerical example is given to testify the feasibility of the method. For the sorting method, the emphasis is laid upon fuzzy quadratic programming problem contained with the intuitionistic fuzzy coefficient.