Parallel fuzzy inference based on α-level sets and generalized means

In this paper, a parallel fuzzy-inference method is proposed in which inference consequences are unified on the basis of α-level sets and generalized means. It has the following advantages over conventional methods: (1) it can control the degree to which the fuzziness and specificity of given facts are reflected to those of unified inference consequences, (2) it can deduce unified inference consequences in the form of normal and convex fuzzy sets which can thus be treated as fuzzy numbers, and (3) it effectively matches systems that include fuzzy-set operations based on the extension principle. This paper first reviews the generalized mean and describes the computational steps of the proposed inference method. Then, the properties of this method are investigated, and the control mechanism of the fuzziness and specificity in unified inference consequences, reflecting those in given facts, are presented. The efficient inference computations are also provided, taking advantage of the α-level-set-based scheme of the proposed inference method. Next, a learning algorithm is derived for the proposed inference method based on the error back-propagation. By feeding fuzzy exemplar patterns, it can automatically adjust the above-mentioned degree of fuzziness and specificity as well as the fuzzy sets in conditional propositions. The simulation studies show the feasibility of the proposed inference method.