Fuzzy Finite Automata Research Articles

An Intuitionistic Fuzzy Finite Automaton on Homomorphism and Admissible relation

An intuitionistic fuzzy finite automaton with an unique membership transition on an input symbol IFA-UM is considered. IFA-UM homomorphism and strong homomorphism are defined. Admissible relation on the set of states of an IFA-UM is characterized. Each admissible relation on an IFA-UMA, finds an IFA-UM A1 and there is a strong homomorphism from A to A1 .

Fuzzy local ω-systems

The natural language computing today demands for the study of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, the concept of fuzzy local ω-language, Büchi fuzzy local ω-language, and some closure properties of fuzzy local ω-languages are presented. We introduce deterministic fuzzy finite automaton with different acceptance mode on fuzzy ω-languages and establish the relationship between these various classes of fuzzy ω-languages. We have defined deterministic fuzzy local automaton and also establish relationships between deterministic fuzzy local automaton, fuzzy local ω-language and Büchi fuzzy local ω-language. Further we show that every fuzzy regular ω-language is a projection of a Büchi fuzzy local ω-language.

Algebraic properties of L-fuzzy finite automata

Fuzzy automata theory on lattice-ordered monoids was introduced by Li and Pedrycz. Dropping the distributive laws, fuzzy finite automata (L-FFAs for short) based on a more generalized structure L, named a po-monoid, are presented and investigated from the view of algebra in this paper. The notions of (strong) successor and source operators, fuzzy successor and source operators which are shown to be closure operators on certain conditions are introduced and discussed in detail. Using the weak primary submachines, a unique decomposition theorem of a fuzzy finite automaton based on a lattice-ordered monoid is obtained. Taking L as a quantale, fuzzy subsystems are proved to be the same as fuzzy submachines of an L-FFA. In particular, intrinsic connections between algebraic properties of L and properties of some operators of an L-FFA are discovered. It is shown that the join-preserving property of fuzzy successor and source operators can be fully characterized by the right and left distributive laws respectively, and the idempotence of successor operator can be characterized equivalently by the nonexistence of zero divisors when L is a lattice-ordered monoid.

Fuzzy multiset finite automata and their languages

Inspired by the generalizations from grammars and finite automata to fuzzy grammars and fuzzy finite automata, respectively, we introduce the concepts of fuzzy multiset grammars and fuzzy multiset finite automata (FMFAs), as the generalizations of multiset grammars and multiset finite automata, respectively. The relationship between fuzzy multiset regular grammars and FMFAs is discussed. Furthermore, we define some operations on fuzzy multiset languages, and prove that the family of FMFA languages is closed under the operations.

Construction of fuzzy automata from fuzzy regular expressions

Li and Pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice-ordered monoid, and generalize the well-known results of the classical theory of formal languages. In particular, they have shown that a fuzzy language over an integral lattice-ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton. However, they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression. In this paper we provide such an efficient method. Transforming scalars appearing in a fuzzy regular expression αinto letters of the new extended alphabet, we convert the fuzzy regular expression αto an ordinary regular expression αR. Then, starting from an arbitrary nondeterministic finite automaton A that recognizes the language ‖αR‖ represented by the regular expression αR, we construct fuzzy finite automata Aα and Aαr with the same or even less number of states than the automaton A, which recognize the fuzzy language ‖α‖represented by the fuzzy regular expression α. The starting nondeterministic finite automaton A can be obtained from αR using any of the well-known constructions for converting regular expressions to nondeterministic finite automata, such as Glushkov–McNaughton–Yamada's position automaton, Brzozowski's derivative automaton, Antimirov's partial derivative automaton, or Ilie–Yu's follow automaton.

Modeling and Formalization of Fuzzy Finite Automata for Detection of Irregular Fire Flames

Fire-flame detection using a video camera is difficult because a flame has irregular characteristics, i.e., vague shapes and color patterns. Therefore, in this paper, we propose a novel fire-flame detection method using fuzzy finite automata (FFA) with probability density functions based on visual features, thereby providing a systemic approach to handling irregularity in computational systems and the ability to handle continuous spaces by combining the capabilities of automata with fuzzy logic. First, moving regions are detected via background subtraction, and the candidate flame regions are then identified by applying flame color models. In general, flame regions have a continuous irregular pattern; therefore, probability density functions are generated for the variation in intensity, wavelet energy, and motion orientation and applied to the FFA. The proposed algorithm is successfully applied to various fire/non-fire videos, and its detection performance is better than that of other methods.

An improved algorithm for determinization of weighted and fuzzy automata

For a given weighted finite automaton over a strong bimonoid we construct its reduced Nerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics. We show that the reduced Nerode automaton is even smaller than the Nerode automaton, which was previously used in determinization related to this semantics. We determine necessary and sufficient conditions under which the reduced Nerode automaton is finite and provide an efficient algorithm which computes the reduced Nerode automaton whenever it is finite. In determinization of weighted finite automata over semirings and fuzzy finite automata over lattice-ordered monoids this algorithm gives smaller crisp-deterministic automata than any other known determinization algorithm.

Formal power series and regular operations on fuzzy languages

In this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet, and representation of fuzzy languages by these formal power series. This representation generalizes the well-known representation of fuzzy languages by their cut and kernel languages. We show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages. We use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata, and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series.

Fuzzy Finite Automata and Monadic Second-Order Lukasiewicz Logic

The authors introduce monadic second-order(MSO-) Lukasiewicz logic and prove that the behaviors of fuzzy finite automata are precisely the fuzzy languages definable with sentences of the MSO Lukasiewicz logic.This generalizes Buchi's and Elgot's fundamental theorems to fuzzy logic setting.The authors also consider first-order Lukasiewicz logic and show that star-free fuzzy languages and aperiodic fuzzy languages introduced here coincide with the first-order definable ones.

Optimize method of minimizing fuzzy finite automata

The existing methods of minimizing fuzzy finite automata do not discuss the transfer and change of the grade of fuzzy automata, but the problem is solved in the optimized method. Firstly, the method transferred from fuzzy finite automata to normal fuzzy automata of a single initial state, and then transferred the normal fuzzy automata into the minimum fuzzy finite automata. Moreover, how the grades of fuzzy states transferred was discussed independently in the transferring methods. Optimizing the method is to make the algorithm simpler and more precise.

Grammar theory based on lattice-ordered monoid

Motivated by Li and Pedrycz's work on fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids and inspired by the close relationship between the automata theory and the theory of formal grammars, we have established a fundamental framework of L -valued grammar. It is shown that the set of L -valued regular languages coincides with the set of L -languages recognized by nondeterministic L -fuzzy finite automata and every L -language recognized by a deterministic L -fuzzy finite automaton is an L -valued regular language.

Intuitionistic fuzzy recognizers and intuitionistic fuzzy finite automata

Intuitionistic fuzzy recognizers and intuitionistic fuzzy finite automata are discussed. The notions of intuitionistic fuzzy recognizer, complete accessible intuitionistic fuzzy recognizer, intuitionistic fuzzy finite automata, deterministic intuitionistic fuzzy finite automata, and intuitionistic fuzzy language are introduced. It is shown that the languages recognized by intuitionistic fuzzy recognizer are regular, and the intuitionistic fuzzy languages recognized by the intuitionistic fuzzy finite automaton and the intuitionistic fuzzy languages recognized by deterministic intuitionistic fuzzy finite automaton are equivalent.

Approximation and robustness of fuzzy finite automata

In previous work we have shown that nondeterministic fuzzy finite automata (or NFFAs, for short) under max-* compositional inference for some t-norm * and deterministic fuzzy finite automata (or DF...

Determinization of fuzzy automata with membership values in complete residuated lattices

In this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices. In comparison with the previous methods, developed by Bělohlávek [R. Bělohlávek, Determinism and fuzzy automata, Information Sciences 143 (2002), 205–209] and Li and Pedrycz [Y.M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005), 68–92], our method always gives a smaller automaton, and in some cases, when the previous methods result in infinite automata, our method can result in a finite one. We also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them, and in particular, to the concept of the Nerode’s fuzzy right congruence of a fuzzy automaton, which we introduce and study here.

Approximation and robustness of fuzzy finite automata

In previous work we have shown that nondeterministic fuzzy finite automata (or NFFAs, for short) under max-∗ compositional inference for some t-norm ∗ and deterministic fuzzy finite automata (or DFFAs, for short) are not necessarily equivalent. We continue to study the approximation and robustness of fuzzy finite automata in this paper. In particular, we show that we can approximate an NFFA by some DFFA with any given accuracy when the NFFA is not equivalent to any DFFA, and the related construction is also presented. Some characterizations of NFFA and DFFA are given. We study the robustness of fuzzy finite automata against imprecision of fuzzy transitions, and some interesting results are obtained.

Fuzzy pushdown automata

Inspired by the similarity of fuzzy regular language to crisp case and the relationship between nondeterministic fuzzy finite automaton and fuzzy regular languages, we study fuzzy pushdown automaton (FPDA) and fuzzy context-free languages (FCFLs). As a generalization, we investigate the movement of one-stack FPDA and discuss the character of multistack FPDA in accepting languages. We get the concept that languages generated by fuzzy context-free K-grammars the languages accepted by one-stack or multistack FPDA are all in the family of FCFL, or say, are usually included in a family of languages generated by A f (K)-fuzzy context-free grammars.

Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids

We study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice-ordered monoid L . For these L -fuzzy finite automata ( L -FFA, for short), we provide necessary and sufficient conditions for the extendability of the state-transition function. It is shown that nondeterministic L -FFA (N L -FFA, for short) are more powerful than deterministic L -FFA (D L -FFA, for short). Then, we give necessary and sufficient conditions for the simulation of an N L -FFA by an equivalent D L -FFA. Next, we turn to the closure properties of languages defined by L -FFAs: we establish closure under the regular operations and provide conditions for closure under intersection and reversal, in particular we show that the family of fuzzy languages accepted by D L -FFAs is not closed under Kleene closure operation, and the family of fuzzy languages accepted by N L -FFAs is not closed under complement operation. Furthermore, we introduce the notions of L -fuzzy regular expressions and give the Kleene theorem for N L -FFAs. The description of D L -FFAs by L -fuzzy regular expressions is also given. Finally, we investigate the level structures of L -FFAs. Our results provide some insight as to what extend properties of L -FFAs and their languages depend on the algebraic properties of L .

Characterizations of fuzzy finite automata

In this paper, we establish some important concepts in fuzzy finite automata (FFAs) with bifuzzy property, and clarify their essential relationships. First we present a number of basic definitions and properties in FFAs. We then define a bifuzzy family of subautomata, bifuzzy source and successor operators, as well as demonstrate the bifuzzy topological characterization of FFAs. Also we clarify the relationships between our results and previous ones, and thus derive a relation figure visualizing their connections. Afterwards, we investigate further the bifuzzy separability, retrievability, and homomorphism; fuzzy continuous mapping and open mapping are also incorporated. In particular, we prove a number of equivalent characterizations for these concepts, and expound the relationships amongst them. This also concludes that both the bifuzzy source and successor operators are fuzzy closure operators. We discover that our investigation generalizes, to some extent, the algebraic fuzzy automata elaborated by Malik, Mordeson, and others. Finally, the main results obtained are summarized; the potential applications are indicated, and a number of related problems for further study are addressed.

Minimization algorithm of fuzzy finite automata

In this paper, a class of fuzzy finite automata corresponding to the Mealy type of ordinary automata is formulated, and also two types of statewise equivalence relations are introduced. From the equivalence relations, a minimal form is defined and a minimization algorithm of the Mealy type of fuzzy finite automata is obtained.

Minimization of fuzzy finite automata

In this paper we show that a fuzzy finite automation M 1 has an equivalent minimal fuzzy finite automation M. We also show that M can be chsen so that if M 2 is equivalent to M 1, then M is a homomorphic image of M 2.