Fuzzy inference based on a weighted average of fuzzy sets and its learning algorithm for fuzzy exemplars

This paper proposes a fuzzy inference method based on a weighted average of fuzzy sets. This method has the property of always obtaining the inference consequence in the form of convex fuzzy sets as long as the then-parts of conditional propositions are defined with normal and convex fuzzy sets. This property is quite useful in introducing learning functions to a fuzzy inference scheme, in particular, when fuzzy-input/fuzzy-output pairs are given by convex fuzzy sets as its exemplar patterns. Moreover, the proposed method can clarify the maximum value of the fuzziness in the inference consequences in advance of its inference operations. In multistage-parallel fuzzy-inference form, it can solve the problem of increasing the fuzziness of the inference consequences in every stage, which possibly results in fuzziness explosion. Reflecting the properties mentioned above, a learning algorithm is derived for multistage-parallel fuzzy-inference with fuzzy exemplar patterns given by convex fuzzy sets