On covering of products of fuzzy finite state machines

On Cardinality of the Group of Weak Fuzzy Automaton Isomorphisms

“…The above definition of fuzzy automaton is different from the definition of ( [9], [11], [12], [16]), in the sense of defining µ only. The above definition 2.1 is, in fact, a generalization of the crisp deterministic finite state automaton, whereas definitions in ( [9], [11], [12], [16]) are generalizations of the crisp nondeterministic finite state automaton.…”

“…The above definition 2.1 is, in fact, a generalization of the crisp deterministic finite state automaton, whereas definitions in ( [9], [11], [12], [16]) are generalizations of the crisp nondeterministic finite state automaton. If A = (Q, Σ, µ) is a fuzzy automaton then the fuzzy function µ is extended to a fuzzy function µ…”

“…fuzzy transition function) ( [5], [11], [12], [16], [18], [20]). Structure preserving fuzzy transition functionsisomorphisms in general and homomorphisms in particular -plays crucial role for equivalent and reduction of a fuzzy automaton( [10], [11], [12], [14], [15], [16], [17]). The aim of this paper is to construct all elements of the group of (weak) fuzzy automaton automorphisms.…”

“…It is pointed out, in remark 2.7, that the fuzzy automaton discussed in ( [9], [11], [14], [16], [17]) is unable to derive homomorphism between fuzzy automata corresponding to an identifier. Hence, throughout this paper we used fuzzy automaton, discussed in [10], based on the notion of fuzzy function.…”

On Algebraic Study of Type-2 Fuzzy Finite State Automata

“…Much later a considerably simpler notion of a fuzzy finite state machine (which is almost identical to a fuzzy automata) was introduced by [6,8]. Somewhat different notions were introduced subsequently in [3,4] and [9]. The concept of homomorphism, transformation semigroup, product property play an important role in the study of finite state machine [2].…”