Fuzzy computing unit

We introduce and study a new concept of fuzzy computing unit. This construct is about coping with "negative" (or inhibitory) information and accommodating it in the language of fuzzy sets. The essential concept developed in this study deals with neurons and neural networks exploiting the concept of balanced fuzzy sets. We recall how the membership notion of fuzzy sets can be extended to the [-1,1] range giving rise to balanced fuzzy sets and then summarize properties of augmented (extended) logic operations on these constructs. Extended model of t-norms and t-conorms were defined and their properties were discussed in detail, several pertinent models of the logic connectives were developed and discussed in context of the concept of balanced fuzzy sets. We show that this idea is particularly appealing in neurocomputing as the "negative" information captured through balanced fuzzy sets exhibits a straightforward correspondence with inhibitory processing mechanisms encountered in neural networks. This gives rise to interesting properties of balanced fuzzy computing units and the ensuing topologies of the networks composed of such units. We study generic learning mechanisms suitable for learning in individual units. Illustrative examples concerning topologies, properties and learning of balanced fuzzy units are included.