Minimization algorithm of fuzzy finite automata

Minimization of lattice finite automata and its application to the decomposition of lattice languages

“…It is not surprising to see a lot of research carried out working in this framework. For example, minimization of fuzzy Mealy machine with output is discussed in [5], while the minimization of fuzzy finite automata with two-valued state transition functions is presented in [12]. Likewise the minimization of fuzzy finite automata with crisp final states without output is studied in [3].…”

Minimization of states in automata theory based on finite lattice-ordered monoids

“…Thereafter, there were a considerable number of authors, such as Mordeson and Malik [12,13], Peeva and Topencharov [18,24], and others having contributed to this field. For details, we refer to [11] and especially the recent studies by Cheng and Mo [2], Peeva [19], and Qiu [21]. Also, fuzzy finite automata have many important applications such as in learning system, pattern recognition, neural networks and data base theory [3,[13][14][15][16]22,26].…”

“…There are many papers on the minimization problem of fuzzy finite automata. For example, minimization of Mealy type of fuzzy finite automata is discussed in [2], minimization of fuzzy finite automata with crisp final states without outputs is studied in [1], and minimization of fuzzy machines becomes the subject of [16,17,23,24].…”

The equivalence between fuzzy Mealy and fuzzy Moore machines

“…If so, it is of interest to determine whether they are equivalent in the sense that they exhibit the same fuzzy input-output characteristics. A substantiate amount of research has been done on how to construct minimal states fuzzy machines from a given fuzzy machine [1,4,15,20,24,27], but very little work has been completed as far as the relationships between various notions of fuzzy state machines are concerned. It is worth noting that this issue is important for a suitable choice of fuzzy models (such as fuzzy Mealy machines and fuzzy Moore machines) for a given systems.…”