1. Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products
- Author
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Kohout, Ladislav J.
- Subjects
Mathematics - Logic ,Computer Science - Logic in Computer Science ,Mathematical Physics ,Mathematics - Quantum Algebra ,04A72 ,08A02 ,37F05 - 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 H\'ajek 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., Comment: 13 pages, 4 figures, 4 tables. Invited and refereed paper presented at JCIS 2003 - 7th Joint Conf. on Information Sciences (Subsection: 9th Internat. Conf. on Fuzzy Theory and Technology), Cary, North Carolina, USA; September 2003
- Published
- 2003