On \(L\)-fuzzy automata, coalgebras and dialgebras: associated categories and \(L\)-fuzzy topologies. (English) Zbl 1543.68181
Summary: This paper is towards studying \(L\)-fuzzy automata, coalgebras, and dialgebras from categorical and \(L\)-fuzzy topological points of view, where \(L\) is a complete residuated lattice. Specifically, we introduce the categories of coalgebras and dialgebras and show that the category of \(L\)-fuzzy automata is categories of coalgebras and dialgebras, respectively. Further, we establish the relationships among the \(L\)-fuzzy languages recognized by \(L\)-fuzzy automata, coalgebras, and dialgebras and study bisimulation between coalgebras. Interestingly, \(L\)-fuzzy languages recognized by \(L\)-fuzzy automaton, coalgebra, and dialgebra are enriched with \(L\)-fuzzy co-topologies and \(L\)-fuzzy topologies.
MSC:
| 68Q45 | Formal languages and automata |
| 18B20 | Categories of machines, automata |
| 54A40 | Fuzzy topology |
Keywords:
complete residuated lattice; \(L\)-fuzzy automaton; \(L\)-fuzzy language; \(L\)-fuzzy topology; homomorphismReferences:
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