Fuzzy neuron modeling based on algebraic approach to fuzzy sets

Wladyslaw Homenda; Witold Pedrycz

doi:10.1117/12.211824

13 June 1995 Fuzzy neuron modeling based on algebraic approach to fuzzy sets

Wladyslaw Homenda, Witold Pedrycz

Proceedings Volume 2493, Applications of Fuzzy Logic Technology II; (1995) https://doi.org/10.1117/12.211824
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

Emerging approaches to modeling fuzzy neurocomputing are solely based on logic operators and/or represented by min and max operators and their extensions--triangular norms. The max-min based models of fuzzy neurons suffer from a kind of insensitivity: only the weakest (strongest) argument(s) affects the result of min (max) operator. While this feature could be taken as an advantage in some cases, in genral it may produce highly undesireable results. Aggregating inputs of a neuron with max-min model results in ignoring most of incoming pieces of information. On the other hand, replacing max-min operations by triangular norms, though removing insensitivity drawback, creates a problem related to a relevant handling of negative nature of information to be processed in neural network. In this paper, new fuzzy-set oriented model of neuron is introduced and analyzed. The architecture of this neuron is based on the selection of positive and negative types of information. The idea of such selection was applied in fuzzy neurons introduced by Hirota and Pedrycz and Pedrycz and Rocha. While the models of those neurons involve max and min operators and triangular norms, the neuron presented here utilizes a certain extension of fuzzy sets. This extension is based on algebraic operators rather than on triangular norms. Subsequently, the formalism is capable of representing negative as well as repetitive information--an evident advantage over conventional fuzzy set connectives. Moreover, processing fuzzy information with aglebraic operators is compatible with the nature of common models of nonfuzzy neurons. Main features of introduced models of neuron are presented and some characteristics of the neuron are discussed. The comparison with other models of fuzzy neurons is also summarized.

Citation Download Citation

Wladyslaw Homenda and Witold Pedrycz "Fuzzy neuron modeling based on algebraic approach to fuzzy sets", Proc. SPIE 2493, Applications of Fuzzy Logic Technology II, (13 June 1995); https://doi.org/10.1117/12.211824

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