Analysis of the operators involved in the definition of the implication functions and in the fuzzy inference process

This paper analyzes the performance of some fuzzy implications proposed in the bibliography together with the operators needed for their definition and for the fuzzy inference process, Examining the specialized literature, it is clear that the selection of the best fuzzy implication operator has become one of the main question in the design of a fuzzy system, being occasionally contradictory (at presently there are more than 72 fuzzy implication proposed and investigated). An approach to the problem from a different perspective is given. The question is to determine whether the selection of the fuzzy implication operator is more important with respect to the behaviour of the fuzzy system than the operators (mainly T-norm, T-conorm and defuzzification method) involved in the definition of the implication function and in the rest of the inference process. The relevance and relative importance of the operators involved in the fuzzy inference process are investigated by using a powerful statistical tool, the ANalysis Of the VAriance (ANOVA) [Box et al., Statistics for experiments: an introduction to design, data analysis and model building, Wiley, New York, 1978; Montgomery, Design and Analysis of Experiments, Wiley, New York, 1984]. © 1998 Elsevier Science Inc. All rights reserved.