Fuzzy Inference Systems: A Critical Review

Fuzzy inference systems represent an important part of fuzzy logic. In most practical applications (i.e., control) such systems perform crisp nonlinear mapping, which is specified in the form of fuzzy rules encoding expert or common-sense knowledge about the problem at hand. This paper shows an equivalence between fuzzy system representation and more traditional (mathematical) forms of function parameterization commonly used in statistics and neural nets. This connection between fuzzy and mathematical representations of a function is crucial for understanding advantages and limitations of fuzzy inference systems. In particular, the main advantages are interpretation capability and the ease of encoding a priori knowledge, whereas the main limitation is the lack of learning capabilities. Finally, we outline several major approaches for learning (estimation) of fuzzy rules from the training data.