A categorical approach to lattice-valued fuzzy automata☆
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Cited by (34)
On compositions of (L-fuzzy) automata: A categorical approach
2024, Fuzzy Sets and SystemsOn L-fuzzy automata, coalgebras and dialgebras: Associated categories and L-fuzzy topologies
2023, Fuzzy Sets and SystemsCitation Excerpt :Specifically, there has been much research dealing with the categorical approach to automata theory (cf., [4,6,9,13,17]). Similar to the automata theory, the category theory has shown to be helpful in the study of fuzzy automata (cf., [3,30,36–38,51,52,55,56,61,62,67]). Among these studies, Tang, Luo and Tang in [55] studied the categories of lattice-valued finite state machines, quasi-lattice-valued transformation semigroups, lattice-valued transformation semigroups, and lattice-valued transformation monoids alongwith functors among them; Močkǒr [36] has provided a method of reduction for fuzzy automata and used the categorical approach to give some uniform treatment (or comparisons) of the varied definition of fuzzy automata in [37,38].
L<sup>B</sup>-valued general fuzzy automata
2022, Fuzzy Sets and SystemsOn the category of L-fuzzy automata, coalgebras and dialgebras
2021, Fuzzy Sets and SystemsCitation Excerpt :The fuzzy automata studied by Močkǒr had no initial and final states, and thus the fuzzy languages associated with them were not considered. For the categorical study of fuzzy automata with initial and final states, Abolpour and Zahedi [3] studied the categorical issues of the general fuzzy automata based on a complete residuated lattice; Li in [32] studied some uniform categorical theoretical treatment of lattice-valued fuzzy automata using quantale theory; Xing and Qiu [65] studied the categorical issue of L-valued automata over a complete residuated lattice and established the relationships between the category of L-valued automata and the category of non-deterministic automata. In the recent years, by using the concepts from category theory, minimal realization for fuzzy languages by using the concept of a crisp-deterministic fuzzy automaton (deterministic automaton equipped with a fuzzy set of final states) was studied in [55,56,59,60].
A categorical approach to minimal realization for a fuzzy language
2018, Fuzzy Sets and SystemsCitation Excerpt :In the present study, we provide a general theory of minimal realization for a given fuzzy language in general category theory setting. Similar to automata theory, the usefulness of category theory in the study of fuzzy automata has been demonstrated in previous studies by [1,24,30–32,48]. In particular, Močkǒr [30] provided a method for reducing fuzzy automata that is analogous to a method for the minimization of classical Moore type automata.
Nondeterministic fuzzy automata with membership values in complete residuated lattices
2017, International Journal of Approximate Reasoning
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This work is supported by National Science Foundation of China (Grant No. 60174016, 10226023), “TRAPOYT” of China and National 973 Foundation Research Program (Grant No. 2002CB312200).