Multiple Criteria Decision Making Method Based On The Intuition Of Triangular Fuzzy Number

There are a lot of Fuzzy Multi-criteria Decision-making (FMCDM) problems in the social and economic activities. And Intuitionistic Fuzzy Multi-criteria Decision-making problems are one important branch of them. So far, researches on intuitionistic fuzzy set based fuzzy multi-criteria decision-making have gained much progress. However, there are only few studies of intuitionistic fuzzy numbers based multi-criteria decision-making problems. Intuitionistic fuzzy numbers can efficiently express the opinions of decision makers, which makes the researches on the multi-criteria decision making problems where the criteria values are intuitionisitc fuzzy numbers have great significance.Based on summarizing and analyzing research achievements of predecessors, the current theories relevent to triangle intuitionistic fuzzy numbers are improved and completed. Based on this work, fuzzy multi-criteria decision-making problems based on triangle intuitionistic fuzzy numbers are studied in-depth. The corresponding decision making models for those problems are constructed and solved. The main work and details are as follow:(1) Arithmetic operations of triangle intuitionistic fuzzy numbers are improved and the new one is proposed. Scoring function, precise function of triangle intuitionistic fuzzy numbers are defined, and the method of comparison of triangle intuitionistic fuzzy numbers is given. In addition, OWA operator of triangle intuitionistic fuzzy numbers, denoted as ITROWA is proposed and relevent theorem of it is proved. Then the definition of triangle intuitionistic fuzzy judgment matrix is proposed and consistency conditions as well as constuction method of it are studied. On this basis, intuitionistic fuzzy multi-criteria decision making methods based on triangle intuitionistic fuzzy judgment matrix are investigated, setting up two decision making models for the problems where the preference information is given with triangle intuitionistic fuzzy judgment matrix, and the criteria values are triangle intuitionistic fuzzy numbers.(2) Triangle intuitionistic fuzzy multi-criteria decision making problems where criteria values are missing or criteria are correlative are investigated. As for the situation in which the criteria values are missing, the interval belief degrees and fuzzy evidential reasoning analytical algorithm are introduced, and for the problem where criteria values are nonlinear additive, Choquet integral which is one of fuzzy integral are introduced. Two kinds of nonlinear aggregation method are proposed for those above problems respectively.(3) The improved logic operators of triangle intuitionistic fuzzy number are defined, and some theorem relative to the operators are given and proved. The defined operators can applied into failure analysis of system very well, and are improvement of current logic operations of triangle intuitionistic fuzzy numbers. The improved operators not only take consideriton of importance relative to the ordered positions of aggragated elements, but also are soft in some way. They are applied into the Fault Tree Analysis of PCBA system and compared with other methods to validate their practicality and rationality.