Analysis of response abilities of fuzzy systems based on non-singleton fuzzifier method

The response properties of fuzzy systems generalized by non-singleton fuzzifier method are discussed. Firstly, the fuzzy system with non-singleton fuzzifier, CRI method and centroid defuzzifier is discussed. A sufficient and necessary condition of the corresponding fuzzy system possessing interpolation properties is deduced. Furthermore, some sufficient conditions of fuzzy system possessing fitted properties are obtained. Then, fuzzy system with non-singleton fuzzifier, triple I method and centroid defuzzifier is studied. It is proved that fuzzy system with non-singleton fuzzifier, regular implication and triple I method is equivalent to Mamdani fuzzy system. And it also possesses interpolation properties. At last, a simulation result is provided to illustrate the validity of the conclusion.