An Approach to Composition Based MISO Algorithms for Fuzzy Inference Schemes Based on the View of Weighted Information

In this article, we will construct multiple-input, single-output (MISO) algorithms for fuzzy inference schemes based on the techniques of aggregation of weighted information. First, by an example, we examine various aspects of a crisp discrete multivariable function under fuzzy environment and obtain many its new functional representations. Next, following the merits of such representations, we build four classes of (new) composition based MISO algorithms as a realization of fuzzy interpolation (extension) of the previous new functional representations, in which, the class of Mamdani-type MISO algorithms are rediscovered. Finally, as an application, we provide an alternative approach to the equivalence conditions of some fuzzy inference methods issued by Seki and Mizumoto recently. In Seki and Mizumoto's approach, they showed that three widely used as fuzzy control methods-the product-sum-gravity method, the simplified fuzzy inference method and the fuzzy singleton-type inference method, are equivalent to each other; and obtained some equivalence conditions between these three methods with two other fuzzy inference methods, while in our approach, we show that all these fuzzy inference methods are closely related with a MISO algorithm of specific type.