A Three-dimsension Expression Of Vague Set And Research

Vague Sets Theory proposed by W. L. Gau and D. J. Buehrer , Taiwan scholars,in 1993, is the development of Fuzzy Sets Theory.Because Vague set is "double fuzzy",we think that if replace membership function by membership function and , we can use all the theory about Fuzzy set in Vague Set's research work. The study of Vague Set's theory and the paper "a three-dimsension expression of Vague Set and research" was processed based on above theory.By proposing a three-dimsension expression of Vague Set ,we research Vague Set's properties and definitions in a new sight.We research the important technology , measure of similarity, entropy; defuzzification, approximate reasoning, of Vague Sets Theory based on the three-dimsension expression of Vague Set.We gave a new general method of measure of similarity based on three-dimsension expression of Vague Set .This kind of method use two values to describe the similarity of two Vague Sets ,can use all similarity measure method based on fuzzy set, and have more fuzzy informations.We research approximate reasoning method based on above method of similarity measure.We proposed a new general characteristics of entropy of Vague sets ,and gave a new entropy function based on the three-dimsension expression of Vague Set.which is simple,and can also be used in fuzzy set,and is more like real world.We proposed a new general method of defuzzification based on the three-dimsension expression of Vague Set ,and proposed a new reasoning method based on the three-dimsension expression of Vague Set .At last,we design a fuzzy control system based on above vague set theorys.