Multi-attribute Decision Making Research And Application Based On AFS Theory

In essence, multi-attribute decision making (MADM) makes use of existing decision information to sort and merit a batch of schemes which to be selected through a certain way. Recent years, multi-attribute decision making problem has become one of the most concerned problems and the solutions under study have been applied to various fields successfully, especially in management which have solved many practical problems. Now the methods used commonly are Data Envelopment Analysis (DEA), Analytic Hierarchy Process (AHP) and Technique for Preference by Similarity to the Ideal Solution (TOPSIS).AFS (Axiomatic Fuzzy Set) theory firstly proposed by professer Xiaodong Liu in 1995 makes ideas of fuzzy set into mathematical axiomatic and is a more realistic mathematical tools. AFS theory provides three new mathematical objects:AFS algebras, AFS structures and cognitive domain.AFS algebra and AFS structure can convert the information in the training examples into the membership functions and their fuzzy logic systemss effectively, and the membership functions and their fuzzy logic operations are directly determined based on the distribution of original data. AFS theory systematically studies and explores in depth the science of fuzzy concept, the unified approach of establishment and the correct representions of the logic of human thought. so that the establishment of the membership function and the fuzzy logic are more objective, rigorous and uniform. Recent years, AFS fuzzy theory has been developed further and has been applied to pattern recognition,fuzzy decision tree and fuzzy control, etc, which are fully showed the practicability and superiority of AFS fuzzy theory.This paper proposed methods used commonly to solve multi-attribute decision making problems DEA,AHP and TOPSIS combining with AFS fuzzy theory to analyze and improve.First, applying AFS theory to analysis and research the evaluation results based on DEA that gives the effective unit an appropriate fuzzy description which provides a reasonable explanation and basis for the evaluation results by DEA. Second, using AFS theory combined with AHP method to calculate the weighted value of index (attributes).Third, using TOPSIS method to make a final evaluation.Experimental results indicate that the method is feasible, operable and also gets accurate and objective evaluation results.