Approximation Of Fuzzy Numbers And Its Application To Multi-Criteria Decision Making Method

Making decision analysis in fuzzy environment, decision makers often use complex fuzzy numbers to describe the decision information. In order to reduce the difficulty of processing fuzzy information, it is necessary to use simple fuzzy numbers to approximate complex fuzzy numbers. In decision analysis process, it is required to evaluate the alternatives, which is solved by using an effective way of ranking fuzzy numbers. For complex fuzzy multi-criteria decision making problems, the methods of simple fuzzy approximation and ranking fuzzy numbers are very important tools to deal with decision information. The main research work and results in this thesis are as follows:(1) By preserving some important indexes of original fuzzy numbers, the thesis studies two trapezoidal approximations of general fuzzy numbers. The first method is proposed to preserve area fuzziness of original fuzzy numbers based on Euclidean distance, the second method is proposed to preserve possibility average value of original fuzzy numbers based on index distance, and then the thesis discusses some important properties of the two approximation algorithms.(2) To fuzzy-typed intuitionistic fuzzy number, based on Euclidean distance, the thesis proposes an interval-valued intuitionistic fuzzy approximation of fuzzy-typed intuitionistic fuzzy number, and then discusses some important properties of the approximation algorithm.(3) Considered from two-dimensional geometry angle, the thesis studies the ranking method of interval-valued intuitionistic fuzzy numbers. Based on the geometry characteristics of membership degree and non-membership degree of interval-valued intuitionistic fuzzy number, a new ranking index is constructed and used to rank interval-valued intuitionistic fuzzy numbers, the ranking method is illustrated by numerical examples and compared with other methods to show its validation and practicality.(4) Fuzzy multi-criteria decision-making problems are researched on the basis of general fuzzy numbers or fuzzy-typed intuitionistic fuzzy numbers. By using the proposed trapezoidal approximation or interval-valued intuitionistic fuzzy approximation, complex fuzzy decision matrix is first translated into simple fuzzy decision matrix, and then two multi-criteria fuzzy decision making methods are given in this thesis, some numerical examples are given to show their practicality finally.