Reciprocity and Duality in a Fuzzy Network Model

P. Saha and A. Konar


Reciprocity, duality, fuzzy logic networks, bidirectional iff relation


This article presents two important characteristics of reasoning that may be employed in the next-generation expert systems using a specialized fuzzy network model. The first characteristic, called reciprocity, ensures computational consistency in the bidirectional iff-type reasoning on a fuzzy network. The condition of reciprocity derived in this article establishes a relationship between the structural topology of the network and the relational matrices of the rules embedded in the network. The second characteristic, called duality, helps in determining the membership distribution of all the negated predicates, when the distribution of one or more negated predicates in the network is supplied. The concept of duality presented is a fuzzy extension of contraposition identity of predicate logic. The authors emphasize the primal–dual relationship with respect to a given fuzzy network. The concepts presented have been applied in an illustrative diagnostic system.

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