Analytic expression of Mamdani fuzzy system constructed by fuzzy similarity degree and its output algorithm
Guijun Wang, Tong Yue Gao, Gang Sun · Journal of Intelligent & Fuzzy Systems · 2019
Fuzzy similarity degree is a measurement of the similarity between fuzzy sets through local information, it plays an important role in the design of fuzzy system and controller. This article first proposes a new computational formula for membership functions of a consequent fuzzy set based on fuzzy similarity degree, and an analytic representation of the Mamdani fuzzy system is obtained through the Gauss fuzzification, product inference engine and center average defuzzification. Next, a specific Mamdani fuzzy system constructed by Gauss fuzzifier or singleton fuzzification be expressed through a given fuzzy similarity degree in practice. Finally, the output algorithm of the proposed fuzzy system is given by the space positioning method. The result shows that the Mamdani fuzzy system constructed by fuzzy similarity degree and Gauss fuzzification is superior to that based on singleton fuzzification in terms of approximation capability.