Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products
<|reference_start|>Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products: 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.<|reference_end|>
@article{kohout2003defining,
    title={Defining Homomorphisms and Other Generalized Morphisms of Fuzzy
  Relations in Monoidal Fuzzy Logics by Means of BK-Products},
    author={Ladislav J. Kohout},
    journal={arXiv preprint arXiv:math/0310175},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0310175},
    primaryClass={math.LO cs.LO math-ph math.MP math.QA}
}