Ruhela, S.; Syropoulos, A.; Yadav, V.; Kumari, M.; Verma, S.; Yadav, S.; Sharma, B. Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations. Preprints2023, 2023081133. https://doi.org/10.20944/preprints202308.1133.v1
APA Style
Ruhela, S., Syropoulos, A., Yadav, V., Kumari, M., Verma, S., Yadav, S., & Sharma, B. (2023). Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations. Preprints. https://doi.org/10.20944/preprints202308.1133.v1
Chicago/Turabian Style
Ruhela, S., Swati Yadav and Binod Sharma. 2023 "Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations" Preprints. https://doi.org/10.20944/preprints202308.1133.v1
Abstract
The aim of this work is to broaden the theory of computation by making use of fuzzy sets and multisets, which are generalization of ordinary sets. We study fuzzy multiset finite automata (FMFA), which are characterized by the incorporation of vagueness when it comes to the choice of the next state and multiple occurrences of the same input symbol. The resulting automaton is a genaralization of both classical automata and fuzzy automata. We discuss the algebraic characteristics of FMFA sub-automata—separatedness, strongly connectedness, cyclic, directable, and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on state set of FMFA. Intrestingly, for a given FMFA, a new FMFA can be constructed that is a homomorphic image of the original FMFA. We define different posets structures that can be associated with a given FMFA and show that some of them are upper semilattices and discuss the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a posets/FUSL associated with a given FMFA. Finally, we introduce the concept of decomposition of a FMFA in two different ways and characterize the strongly connected, triangular and directable FMFA.
Keywords
Fuzzy Multiset finite automaton; Subautomaton of a FMFA; Upper semi-lattices; Strongly connected FMFA; Lower set; Principle lower set; Decomposition of a FMFA.
Subject
Computer Science and Mathematics, Computer Science
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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