General fuzzy automata based on complete residuated lattice-valued. (English) Zbl 1398.68289
Summary: The present paper has been an attempt to investigate the general fuzzy automata on the basis of complete residuated lattice-valued (\(L\)-GFAs). The study has been chiefly inspired from the work by Mockor. Regarding this, the categorical issue of \(L\)-GFAs has been studied in more details. The main issues addressed in this research include: (1) investigating the relationship between the category of \(L\)-GFAs and the category of non-deterministic automata (NDAs); as well as the relationship between the category of generalized \(L\)-GFAs and the category of NDAs; (2) demonstrating the existence of isomorphism between the category of \(L\)-GFAs and the subcategory of generalized \(L\)-GFAs and between the category of \(L\)-GFAs and the category of sets of NDAs; (3) and further scrutinizing some specific relationship between the output \(L\)-valued subsets of generalized \(L\)-GFAs and the output \(L\)-valued of NDAs.
Keywords:
general fuzzy automata; active state set; residuated lattice; isomorphism of category; functorReferences:
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