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On the category of L-fuzzy automata, coalgebras and dialgebras
- Source :
- Fuzzy Sets and Systems. 420:1-28
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- This paper is towards the study of L-fuzzy automata from the categorical point of view, where L is a complete residuated lattice. We introduce a functor having both the left/right adjoint from the category of L-fuzzy Σ-semiautomata LFSA ( Σ ) to the category LFTCRL(Σ), a category of complete residuated lattices corresponding to L-fuzzy Σ-semiautomata. The L-fuzzy response map of an L-fuzzy automaton leads us to provide a characterization of an L-fuzzy regular language. Interestingly, we show that the category LFSA ( Σ ) is a category of T 1 -coalgebras/ ( T 2 , T 3 ) -dialgebras. Moreover, we establish a relationship between the category of T 1 -coalgebras and the category of ( T 2 , T 3 ) -dialgebras.
- Subjects :
- Fuzzy automata
0209 industrial biotechnology
Pure mathematics
Functor
Logic
02 engineering and technology
Characterization (mathematics)
Automaton
020901 industrial engineering & automation
Regular language
Artificial Intelligence
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
Point (geometry)
Residuated lattice
Categorical variable
Mathematics
Subjects
Details
- ISSN :
- 01650114
- Volume :
- 420
- Database :
- OpenAIRE
- Journal :
- Fuzzy Sets and Systems
- Accession number :
- edsair.doi...........22ccb3c78b0ae250d2aec28b57dd3b23