Fuzzy Finite Automata Research Articles

Polynomial crisp-minimization algorithm for fuzzy deterministic automata

Designing automata minimization algorithms is a significant topic in Automata Theory and Languages with practical applications. In this paper, we develop an efficient minimization algorithm for deterministic fuzzy finite automata over locally finite lattices. More precisely, the algorithm outputs an equivalent minimal crisp-deterministic fuzzy finite automaton for an input fuzzy deterministic finite automaton (FDfA). The running time of the proposed algorithm is polynomial for particular types of locally finite lattices, specifically for max-min-based complete residuated lattices. The intuition behind the proposed algorithm relies on the polynomial minimization algorithm's intuition for ordinary deterministic automata developed by Vazquez de Parga, Garcia, and Lopez (2013) [35]. The motivation for this study comes from the fact that the original algorithm's notions and meanings are lost in the context of fuzzy automata. Thus, we establish a new theoretical foundation that provides the correctness and the polynomial-time nature of this new crisp-minimization algorithm for FDfAs.

Generalized rough and fuzzy rough automata for semantic computing.

The classical automata, fuzzy finite automata, and rough finite state automata are some formal models of computing used to perform the task of computation and are considered to be the input device. These computational models are valid only for fixed input alphabets for which they are defined and, therefore, are less user-friendly and have limited applications. The semantic computing techniques provide a way to redefine them to improve their scope and applicability. In this paper, the concept of semantically equivalent concepts and semantically related concepts in information about real-world applications datasets are used to introduce and study two new formal models of computations with semantic computing (SC), namely, a rough finite-state automaton for SC and a fuzzy finite rough automaton for SC as extensions of rough finite-state automaton and fuzzy finite-state automaton, respectively, in two different ways. The traditional rough finite-state automata can not deal with situations when external alphabet or semantically equivalent concepts are given as inputs. The proposed rough finite-state automaton for SC can handle such situations and accept such inputs and is shown to have successful real-world applications. Similarly, a fuzzy finite rough automaton corresponding to a fuzzy automaton is also failed to process input alphabet different from their input alphabet, the proposed fuzzy finite rough automaton for SC corresponding to a given fuzzy finite automaton is capable of processing semantically related input, and external input alphabet information from the dataset obtained by real-world applications and provide better user experience and applicability as compared to classical fuzzy finite rough automaton.

Two dimensional fuzzy regular languages

A two dimensional string is called a picture and is defined as a rectangular array of symbols taken from a finite alphabet. A two dimensional language or a picture language is a set of pictures. In this paper, a theoretical study is reported for two dimensional fuzzy regular languages generated by two dimensional fuzzy regular grammars and the two dimensional fuzzy finite state automata for the two dimensional fuzzy regular languages. We can construct the two dimensional fuzzy finite state automaton from the given two dimensional fuzzy regular grammar and vice versa. Further, we discuss some of the closure properties of two dimensional fuzzy regular languages with examples. We discuss the applications of two dimensional fuzzy regular language with respect to kolam patterns.

An Interval Type-2 Fuzzy Model of Computing with Words via Interval Type-2 Fuzzy Finite Rough Automata with Application in COVID-19 Deduction

Classical automata, fuzzy automata, and rough automata with input alphabets as numbers or symbols are formal computing models with values. Fuzzy automata and rough automata are computation models with uncertain or imprecise information about the next state and can only process the string of input symbols or numbers. To process words and propositions involved in natural languages, we need a computation model to model real-world problems by capturing the uncertainties involved in a word. In this paper, we have shown that computing with word methodology deals with perceptions rather than measurements and allows the use of words in place of numbers and symbols while describing the real-world problems together with interval type-2 (IT2) fuzzy sets which have the capacity to capture uncertainties involved in word using its footprint of uncertainty. The rough set theory, which has potential of modeling vagueness in the imprecise and ill-defined environment, introduces a computation model, namely, IT2 fuzzy rough finite automata, which is efficient to process uncertainties involved in words. Further, we have shown the application of introduced IT2 fuzzy finite rough automaton in the medical diagnosis of COVID-19 patients.

Intuitionistic fuzzy monoids in an intuitionistic fuzzy finite automaton with unique membership transition on an input symbol

Intuitionistic fuzzy monoids in an intuitionistic fuzzy finite automaton with unique membership transition on an input symbol

Fault Diagnosis in Fuzzy Discrete Event System: IncompleteModels and Learning

Nowadays, determining faults in non-stationary environment and that can deal with the problems of fuzziness impreciseness and subjectivity is a challenging task in complex systems such as nuclear center, or wind turbines, etc. Our objective in this paper is to develop models based on fuzzy finite state automaton with fuzzy variables describing the industrial process in order to detect anomalies in real time and possibly in anticipation. A diagnosis method has for goal to alert actors responsible for managing operations and resources, able to adapt to the emergence of new procedures or improvisation in the case of unexpected situations. The diagnoser module use the outputs events and membership values of each active state of the model as input events.

Fuzzy Regular Languages Based on Residuated Lattice

The purpose of this work is to introduce the concept of fuzzy regular languages (FRL) accepted by fuzzy finite automata, and try to introduce the categorical look of fuzzy languages where the codomain of membership functions are taken as a complete residuated lattice, instead of [Formula: see text]. Also, we have introduced pumping lemma for FRL, which is used to establish a necessary and sufficient condition for a given fuzzy languages to be non-constant.

Computing Fuzzy Bisimulations for Fuzzy Structures Under the Gödel Semantics

Bisimulation is a well-known notion in modal logic and the theory of labeled transition systems. It is used for characterizing indiscernibility between states and has important applications in minimizing structures, separating expressive powers of modal and related logics, as well as concept learning in description logics (DLs). Fuzzy bisimulation is a counterpart of bisimulation for dealing with fuzzy structures. In this article, we present an efficient algorithm with a complexity $O((m+n)n)$ for computing the greatest fuzzy bisimulation between two finite fuzzy interpretations in the fuzzy DL $\mathit {f}\!\mathcal {ALC}$ under the Godel semantics, where $n$ is the number of individuals and $m$ is the number of nonzero instances of roles in the given fuzzy interpretations. We also adapt our algorithm for computing fuzzy bisimulations and simulations between fuzzy finite automata, as well as for dealing with other fuzzy DLs. The resulting algorithms are much more efficient than the previously known ones, as they reduce the complexity from $O(n^5)$ to $O((m+n)n)$ .

Simulation of artificial intelligence in a computer game

Artificial intelligence, implemented in the space of a computer game, will allow performing a variety of practice-oriented tasks and time-consuming algorithms: finding ways, avoiding obstacles, conducting combat, choosing the appropriate strategy, simulating emotions, dialogue, etc. The main problem that should be solved when developing an appropriate gaming application is to simulate the mechanism for controlling all possible functions of the game object. The research methodology includes: analysis of scientific works of Russian and foreign authors; the method of system information analysis, the method of mathematical and information modeling; computer experiment method, as a kind of computational; decision making algorithms. The paper presents a solution to the problem, including the informed choice of a decision-making algorithm, and the design of a model of a fuzzy finite automaton that combines the advantages of a model of a generating finite automaton and fuzzy logic. Based on the results of testing the implemented model, a conclusion was formulated about the main advantage of the artificial intelligence model for the gaming application - its ability to make an unusual decision in the arisen game situation.

General Fuzzy Finite Switchboard Automata

The constructions of finite switchboard state automata are known to be an extension of finite automata in the view of commutative and switching state machines. This research incorporated an idea of a switchboard in the general fuzzy automata to introduce general fuzzy finite switchboard automata. The attained output reveals that a strongly connected general fuzzy finite switchboard automaton is equivalent to the retrievable general fuzzy automata. Further, the notion of the switchboard subsystem and strong switchboard subsystem of general fuzzy finite switchboard automata are examined. Finally, the concept of fuzzy topology on general fuzzy finite switchboard automata in terms of these characterisations is formulated.

A formal model of semantic computing

In the existing works of semantic computing (SC), the word “computing” in the phrase “semantic computing” means computational implementations of semantics reasoning (e.g., ontology reasoning, rule reasoning, semantic query, and semantic search) but is irrelevant to the formal theory of computation (e.g., computational models such as finite automaton, pushdown automaton, and Turing machine). In this paper, we propose a different understanding of “semantic computing” from a computation theory perspective. Concretely, we present a formal model of SC in terms of automata and discuss SC for the two most important and simplest types of automata, namely finite automata and pushdown automata. For each automaton, we first consider a simple case (equivalent concepts) and then we further investigate a general situation (semantically related concepts). That is, some new automata for SC are provided: finite (or pushdown) automaton for SC under equivalent concepts, finite (or pushdown) automaton for SC w.r.t. external words, nondeterministic finite automaton for SC under equivalent concepts (or w.r.t. external words), fuzzy finite (or pushdown) automaton for SC under semantically related concepts, and fuzzy finite (or pushdown) automaton for SC w.r.t. external words. Furthermore, we give some properties of these new automata for SC and prove that these new automata are extensions (or enlargements) of traditional (fuzzy) automata.

Conditions for Minimal Fuzzy Deterministic Finite Automata via Brzozowski's Procedure

This paper deals with the application of Brzozowski's minimization procedure to fuzzy finite automata with truth-values in a complete residuated (zero-divisor-free) lattice. For a given fuzzy finite automaton $\mathcal{A}$ , the procedure computes the automaton $d(r(d(r(\mathcal{A})))$ , where $d(\mathcal{A})$ is a (fuzzy) determinization of $\mathcal{A}$ , and $r(\mathcal{A})$ is the reverse automaton of $\mathcal{A}$ . It is observed that the size of the resulting automaton is strongly dependent on the determinization method used in the procedure. Consequently, this paper studies necessary and sufficient conditions for obtaining minimal fuzzy deterministic finite automata via Brzozowski's procedure. The study is accomplished for determinization methods based on a generalized notion of accessible fuzzy subset construction. The obtained conditions determine that Brzozowski's procedure returns a minimal fuzzy deterministic finite automaton when the determinization method does not produce proportional fuzzy states. This is the reason to obtain minimal fuzzy deterministic finite automata using Brzozowski's procedure for fuzzy finite automata with truth-values in the product-structure when the determinization method is the method based on factorization of fuzzy states.

Quantitative model checking of linear-time properties based on generalized possibility measures

Model checking of linear-time properties based on possibility measures was studied in previous work (Li and Li (2013)). However, the linear-time properties considered in the previous work was qualitative and was based on Boolean logic, the linear-time properties containing possibility information (we call it fuzzy linear-time properties here, which is based on fuzzy logic) of system could not be represented and tackled using the previous methods. We shall study quantitative model checking of fuzzy linear-time properties based on generalized possibility measures in the paper. Both the model of the system, as well as the properties the system needs to adhere to, are described using possibility information to identify the uncertainty in the model/properties. The systems are modeled by generalized possibilistic Kripke structures (GPKS, in short), and the properties are described by fuzzy linear-time properties. Concretely, fuzzy linear-time properties about reachability, always reachability, constrain reachability, repeated reachability and persistence in GPKSs are introduced and studied. Fuzzy regular safety properties and fuzzy ω-regular properties in GPKSs are introduced, the verification of fuzzy regular safety properties and fuzzy ω-regular properties using fuzzy finite automata are thoroughly studied. It has been shown that the verification of fuzzy regular safety properties and fuzzy ω-regular properties in a finite GPKS can be transformed into the verification of (always) reachability properties and repeated reachability (persistence) properties in the product GPKS introduced in this paper. Several examples are given to illustrate the methods presented in the paper.

Topologies associated to (dual) fuzzy approximation operators on fuzzy finite state automata

Topologies associated to (dual) fuzzy approximation operators on fuzzy finite state automata

Pedestrian’s Intention Prediction Based on Fuzzy Finite Automata and Spatial-temporal Features

Pedestrian’s Intention Prediction Based on Fuzzy Finite Automata and Spatial-temporal Features

Further improvements of determinization methods for fuzzy finite automata

In this paper we provide further improvements of determinization methods for fuzzy finite automata. These methods perform better than all previous determinization methods for fuzzy finite automata, developed by Bělohlávek [3], Li and Pedrycz [38], Ignjatović et al. [25], and Jančić et al. [33], in the sense that they produce smaller automata, while require the same computation time. The only exception is the Brzozowski type determinization algorithm developed recently by Jančić and Ćirić [34], which produces a minimal crisp-deterministic fuzzy automaton, but the algorithms created here can also be used within the Brzozowski type algorithm and improve its performance.

Determinization of Fuzzy Automata by Means of the Degrees of Language Inclusion

Determinization of fuzzy finite automata is understood here as a procedure of their conversion into equivalent crisp-deterministic fuzzy automata, which can be viewed as being deterministic with possible infinitely many states, but with fuzzy sets of terminal states. Particularly, significant determinization methods are those that provide a minimal crisp-deterministic fuzzy automaton equivalent to the original fuzzy finite automaton called canonization methods. One canonization method for fuzzy finite automata, the Brzozowski type determinization, has been developed recently by Jancic and Ciric in [10] . Here we provide another canonization method for a fuzzy finite automaton $\cal A=(A,\sigma, \delta, \tau)$ over a complete residuated lattice $\cal L$ , based on the degrees of inclusion of the right fuzzy languages associated with states of $\cal A$ into the left derivatives of the fuzzy language recognized by $\cal A$ . The proposed procedure terminates in a finite number of steps, whenever the membership values taken by $\delta$ , $\sigma$ , and $\tau$ generate a finite subsemiring of the semiring reduct of $\cal L$ . This procedure is generally faster than the Brzozowski type determinization, and if the basic operations in the residuated lattice $\cal L$ can be performed in constant time, it has the same computational time as all other determinization procedures provided in [8] , [11] , and [12] .

Nonblocking check in fuzzy discrete event systems based on observation equivalence

In this paper, we deal with the synthesis about nonblocking check in fuzzy discrete event systems (FDESs) by using abstraction and observation equivalence of fuzzy finite automaton (FFA). In FDESs, such a check imposes a great computational challenge because of the complexity incurred by the composition of plants and the supervisors. With respect to ideas in modeling control system, we present procedure based on FFA abstractions, which removes internal transitions of irrelevant transitions, allowing the nonblocking check to be performed on relatively small automata.

Learning Diagnosis Based on Evolving Fuzzy Finite State Automaton


 
 
 Nowadays, determining faults (or critical situations) in non- stationary environment is a challenging task in complex systems such as Nuclear center, or multi-collaboration such as crisis management. A discrete event system or a fuzzy discrete event system approach with a fuzzy role-base may re- solve the ambiguity in a fault diagnosis problem especially in the case of multiple faults (or multiple critical situations). The main advantage of fuzzy finite state automaton is that their fuzziness allows them to handle imprecise and uncertain data, which is inherent to real-world phenomena, in the form of fuzzy states and transitions. Thus, most of approaches proposed for fault diagnosis of discrete event systems require a complete and accurate model of the system to be diagnosed. However, in non-stationary environment it is hard or impossible to obtain the complete model of the system. The focus of this work is to propose an evolving fuzzy discrete event system whose an activate degree is associated to each active state and to develop a fuzzy learning diagnosis for incomplete model. Our approach use the fuzzy set of output events of the model as input events of the diagnoser and the output of a fuzzy system should be defuzzified in an appropriate way to be usable by the environment.
 
 

A comment on “Construction of fuzzy automata from fuzzy regular expressions”

The aim of this comment is to point out that the fuzzy language recognized by a nondeterministic finite automaton, which is associated with a fuzzy regular expression, in the context of Stamenković–Ćirić's method (Stamenković and Ćirić (2012) [11]), is recognized by a fuzzy finite automaton with ε-moves. Every fuzzy automaton with ε-moves is also equivalent to a fuzzy automaton and there are effective methods for removing ε-moves in order to obtain the equivalent fuzzy automaton. In this way, our proposal to convert a fuzzy regular expression to a fuzzy finite automaton is based on the construction of a fuzzy automaton with ε-moves for the fuzzy regular expression and the construction of an equivalent fuzzy finite automaton by means of ε-removal operation.