Structure and learning algorithms of a nonsingleton input fuzzy neural network based on the approximate analogical reasoning schema

A novel fuzzy neural network, the pseudo-outer-product-based fuzzy neural network using the nonsingleton fuzzifier together with the approximate analogical reasoning schema (nonsingleton fuzzifier POPFNN–AARS), is proposed in this paper. The nonsingleton fuzzifier POPFNN–AARS is developed as an improvement over the singleton fuzzifier POPFNN–AARS developed by Quek and Zhou [POPFNN–AARS: a pseudo outer-product based fuzzy neural network, IEEE Trans. Systems, Man, Cybernetics 29(6) (1999) 859–870]. The employment of the approximate analogical reasoning schema (AARS) as the fuzzy inference model enables the integration of a nonsingleton fuzzifier in the nonsingleton fuzzifier POPFNN–AARS. Compared against the commonly used singleton fuzzifier, the nonsingleton fuzzifier is more powerful in handling imprecise data. Different similarity measures and modification functions proposed by Zwick et al. [Measures of similarity between fuzzy concepts: a comparative analysis, Internat. J. Approx. Reason. 1 (1987) 221–242] for AARS in the nonsingleton fuzzifier–AARS are investigated. The structure and learning algorithms of the proposed nonsingleton fuzzifier POPFNN–AARS are presented. Several sets of real-life data are used to test the performance of the nonsingleton fuzzifier POPFNN–AARS and their experimental results are presented for detailed discussion.