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Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products

Ladislav J. Kohout
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Abstract

The present paper extends generalized morphisms of relations into the realm of Monoidal Fuzzy Logics by first proving and then using relational inequalities over pseudo-associative BK-products (compositions) of relations in these logics. In 1977 Bandler and Kohout introduced generalized homomorphism, proteromorphism, amphimorphism, forward and backward compatibility of relations, and non-associative and pseudo-associative products (compositions) of relations into crisp (non-fuzzy Boolean) theory of relations. This was generalized later by Kohout to relations based on fuzzy Basic Logic systems (BL) of Hájek and also for relational systems based on left-continuous t-norms. The present paper is based on monoidal logics, hence it subsumes as special cases the theories of generalized morphisms (etc.) based on the following systems of logics: BL systems (which include the well known Goedel, product logic systems; Lukasiewicz logic and its extension to MV-algebras related to quantum logics), intuitionistic logics and linear logics.

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BibTeXRIS

Ladislav J. Kohout. 2003-10-12. Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products. https://arxiv.org/abs/math/0310175

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