Irreducible Fuzzy Multiset Finite Automaton

Abstract

This study aims to investigate the algebraic properties of fuzzy multiset finite automaton (FMFA), giving a congruence relation. Using the equivalence classes, a minimal accessible complete FMFA is then presented. In addition, we define the concepts of admissible relation, admissible partition for FMFA and quotient FMFA. Further, we present an algorithm which determines an admissible partition for an FMFA and we suggest the time complexity of the algorithm. In particular, we introduce a connection between the admissible partition and the quotient FMFA and we show that any quotient of a given FMFA and the FMFA itself have the same language. Furthermore, using the quotient FMFA, we obtain an irreducible FMFA with the same language.

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

“…al. [48,54]; (ii) These cited works mainly focused in multiset based study of (classical/fuzzy) automata, Grammar and regular languages, but algebraic concepts such as subautomaton, source, successor, strongly connected, triangular, composition, decomposition of FMFA and lattice associated with FMFA were still remains to be discussed. However, such algebraic concepts in classical automata theory have been studied by Eilenberg [1], Fleck [2], Holcombe and Holcombe [3], Hopcroft and Ullman [4], Bavel [5], and Fleck [2], whereas lattice theoretic aspects of classical automata have been described by ito [6][7][8], Cirić, and Bogdanović [9], and Atani and Bazari [10] and Cirić, Bogdanović and Petković [11], and in case of fuzzy automata theory algebraic concepts were studied by Mordeson and Malik [19,20] and Jin [21] and lattice theoretic aspects of FFSA have been studied in Tiwari, Yadav, and Singh [22].…”

“…[53], and Shamsizadeh et.al. [54]. Some other computing models based on the theory of multiset can be found in [31,[55][56][57] and references therein.…”

Isomorphism Between Two Vector General Fuzzy Automata

“…Several researchers have contributed to the growth of the fuzzy automata theory. Among these works, the work of Jin and his coworkers (Jin et al, 2013) is directed towards the algebraic study of fuzzy automata based on Po-monoids; the work of Abolpour and Zahedi (Abolpour et al, 2020;Abolpour and Zahedi, 2017) is directed towards the use of categorical concepts in the study of general fuzzy automata with membership values in different lattice structures; the work of Qiu (2001Qiu ( , 2002 is directed towards the algebraic, topological and categorical study of fuzzy automata theory based on residuated lattices; the work of Peeva (1988Peeva ( , 1991 relates to the study of minimizing the states of fuzzy automata and its application to study pattern recognition; the work of Pal and their coworkers (Pal et al, 2019) is directed towards the study of fuzzy automaton based on the residuated and co-residuated lattice, the work of Shamsizadeh and coworkers (Shamsizadeh et al, 2021;Raisi Sarbizhan et al, 2022;Shamsizadeh and Zahedi, 2022;Shamsizadeh, 2022) is directed towards the study of fuzzy automaton based on graph theory and multiset theory and neutrosophic sets; Ghorani, Moghari and coworkers study fuzzy tree automata based on lattice-valued.…”

Vector General Fuzzy Automaton: A Refining Analyzing

“…In his study, Li [14] clearly examined a categorical approach to lattice-valued fuzzy automata. Shamsizadeh and her coworkers studied the graph concept for general fuzzy automata [25,33], and studied and investigated on the minimization of fuzzy multiset finite automaton [31,32]. Doostfatemeh and Kremer [5] introduced the concept of general fuzzy automata to emphasize the insufficiency of the current literature to deal with the applications which in turn depend on fuzzy automata as a modeling tool, assigning membership values to active states of a fuzzy automaton.…”