Two New Methods For Ranking Fuzzy Numbers And Their Applications In Fuzzy Linear Programming

Fuzzy optimization is an optimization problem when objects or constraints appear in fuzzy situations.As an important branch of fuzzy mathematics,fuzzy optimization problem is a very important class of fuzzy optimization problem,which is the problem of fuzzy linear programming(FLP),which has been widely studied by many scholars.In fact,how to determine the order relation of fuzzy numbers is a very important problem in solving fuzzy linear programming problems.In this paper,two new methods for ranking fuzzy numbers are proposed,and the two new ranking methods of fuzzy numbers are applied to the solution of fuzzy linear programming problems.This paper first introduces the related knowledge of fuzzy mathematics,fuzzy optimization and fuzzy linear programming,and the research status and common methods of fuzzy linear programming,such as tolerance method and possibility method,area compensation method proposed by Roubens and fuzzy number sorting method proposed by Yager,etc.Secondly,two new methods for ranking fuzzy numbers are proposed by using bounded product operators.The first method compares the different fuzzy numbers with the specific reference fuzzy number respectively,and uses the size of the comparison to get the order of the fuzzy number.The second comparison method is to compare the fuzzy number and two,and then to the following natural number,the order relation between the fuzzy numbers can be obtained.Then,we compare the two new methods proposed in this paper with the typical fuzzy number sorting methods,and verify the rationality and effectiveness of the new methods for sorting the two fuzzy numbers proposed in this paper by the calculation of some practical examples.Finally,the fuzzy number method is applied to fuzzy linear programming with fuzzy number constraint inequality,and preliminary results are obtained.Through the example that the fuzzy number is triangular fuzzy number,a real example is given to prove the validity of the fuzzy linear programming problem established in this paper.