Fuzzy Regular Languages Research Articles

Two dimensional fuzzy context-free languages and tiling patterns

Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture language) is a collection of two dimensional words, which are a rectangular array of symbols made up of finite alphabets. Two dimensional automata can recognize two dimensional languages that could not be recognized by one dimensional automata. In this paper, we introduce two dimensional fuzzy context-free languages generated by the two dimensional fuzzy context-free grammars and accepted by the two dimensional fuzzy pushdown automata in order to deal with the vagueness that arises in two dimensional context-free languages. We can construct a two dimensional fuzzy context free grammar from the given two dimensional fuzzy pushdown automata and vice versa. In addition, we prove that two dimensional fuzzy context-free languages are closed under union, column concatenation, column star, homomorphism, inverse homomorphism, reflection about right-most vertical, reflection about base, conjugation and half-turn and also show that two dimensional fuzzy context-free languages are not closed under matrix homomorphism, quarter-turn and transpose. Further, we have given the applications and the uses of closure properties in the formation of tiling patterns.

Array generating fuzzy petri nets and rectangular picture languages

A two dimensional language is a collection of two dimensional words, which are rectangular array of symbols made up of finite alphabets. Fuzzy Petri nets are the generalization of classical Petri nets designed to deal with imprecise and ambiguous data which usually occurs in knowledge based systems, image processing, etc. They have been widely used to represent fuzzy production rules and fuzzy rule-based reasoning. In this paper, a new model called array token fuzzy Petri net to generate two dimensional fuzzy regular languages has been introduced. Array token fuzzy Petri nets are used to deal with impreciseness and uncertainties occurring in two dimensional regular languages. Furthermore, proved that for every two dimensional fuzzy regular grammar there exists an array token fuzzy Petri net that generates the same two dimensional fuzzy regular language and also establish some closure properties of the languages generated by array token fuzzy Petri net.

Regular string token fuzzy Petri nets

Fuzzy Petri nets are a type of classical Petri nets designed to deal with imprecise and ambiguous data, that have been widely used to represent fuzzy production rules and fuzzy rule-based reasoning. In this paper, we introduce a new model called string token fuzzy Petri nets to generate fuzzy regular languages. Also, we study the equivalences of fuzzy regular grammar and regular string token fuzzy Petri net and establish some closure properties such as union, catenation, kleene closure, reversal, homomorphism and inverse homomorphism of the languages generated by the regular string token fuzzy Petri nets.

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.

Intuitionistic fuzzy (⊗,N)-general regular languages and their minimization implementation

We firstly give the notion of intuitionistic fuzzy (⊗,N)-general regular languages (IF(⊗,N)-GRLs) under a t-norm ⊗ and a fuzzy negation N and study their properties. The similarities and differences between IF(⊗,N)-GRLs and intuitionistic fuzzy regular languages (IFRLs) are investigated for explaining the existence of intuitionistic fuzzy automata (IFAs) (⊗,N)-recognizing IF(⊗,N)-GRLs. Next, we discuss whether or not the set of IF(⊗,N)-GRLs is closed under the generalized operations shown here. Concretely, the set of IF(⊗,N)-GRLs is closed under the generalized intersection, but not closed under the generalized complement, and the necessary and sufficient condition of closure of that set under the generalized union, the generalized concatenation and the generalized Kleene closure is thought as well. We also deliberate on the Pumping lemma and the Myhill-Nerode theorem in the framework of IF(⊗,N)-GRLs. Finally, we study the minimization implementation of IF(⊗,N)-GRLs, that is, for an IF(⊗,N)-GRL f, if it is (⊗,N)-recognized by a given accessible deterministic intuitionistic fuzzy automaton (DIFA) A, then a polynomial-time algorithm is presented to realize the construction of a minimal DIFA (⊗,N)-recognizing f by using A.

Fuzzy ϵ-approximate regular languages and minimal deterministic fuzzy automata ϵ-accepting them

In this paper, for a real number ϵ∈[0,1], we put forward the notion of fuzzy ϵ-approximate regular languages and study their properties, especially the Pumping lemma in the context of this kind of languages. By comparing sets of fuzzy ϵ-approximate regular languages under the order of set inclusion, we get an (infinite) hierarchy of fuzzy languages, the smallest is the set of fuzzy regular languages and the biggest is the set of fuzzy languages, and the sets of ϵ-approximate regular languages are different for different ϵ∈(0,12). We also investigate whether operations closed in the set of fuzzy regular languages are still closed in the set of fuzzy ϵ-approximate regular languages. Furthermore, for a fuzzy ϵ-approximate regular language f, ϵ-approximate equivalence relations for f are characterized in order to construct deterministic fuzzy automata ϵ-accepting f. If a fuzzy ϵ-approximate regular language f is also a fuzzy regular language and accepted by a given accessible deterministic fuzzy automaton A, then we give a polynomial-time algorithm to construct at least one minimal deterministic fuzzy automaton ϵ-accepting f by means of A. Finally, we point out that the number of states of minimal deterministic fuzzy automata ϵ-accepting a fuzzy regular language is smaller than or equal to that of minimal deterministic fuzzy automata accepting this language.

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.

An Fuzzy Lexical Research

The objective of this paper is to analyse the design and implementation of the fuzzy lexical analyser and observe how it is different from the traditional lexical analyser. It is known that lexical analysis is an important phase of a compiler. It reads the source program character by character and uses regular expressions, finite automata methods for string matching. Unlike traditional lexical analysers, tokens in fuzzy analysers belong to more than one token type with varying degree of membership. The paper exchange views on the design and implementation of fuzzy lexical analysers. It observes algorithms that handle errors due to insertion, deletion etc. in the lexical analysis phase of a compiler. Several properties of fuzzy languages are also reviewed. Hence this paper gives a comprehensive view of fuzzy regular languages, models and algorithms

TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular languages. Moreover, we prove that the induced fuzzy topological space has a basis consisting of leveled characteristic functions of the closure of cut languages of fuzzy regular languages.

Rough Fuzzy Automata and Rough Fuzzy Grammar

Automata theory plays a key role in computational theory as many computational problems can be solved with its help. Formal grammar is a special type of automata designed for linguistic purposes. Formal grammar generates formal languages. Rough grammar and rough languages were introduced to incorporate the imprecision of real languages in formal languages. These languages have limitations on uncertainty. The authors have considered both uncertainty and approximations to define rough fuzzy grammar and rough fuzzy languages. Under certain restrictions, their grammar reduces to formal grammar. Furthermore, the authors have proposed definition of rough fuzzy automata that accepts rough fuzzy regular language.

On minimal realization for a fuzzy language and Brzozowski’s algorithm

The purpose of the present work is to provide a simpler solution of a well-known characterization of fuzzy regular languages and a minimal realization for given fuzzy language by using Brzozowski’s algorithm. In between, we associate two crisp deterministic fuzzy automata with a given crisp deterministic fuzzy automaton and show that the reachability and observability maps of the given crisp deterministic fuzzy automaton turn out to be morphisms of category of all crisp deterministic fuzzy

Prognosis—A Wearable Health-Monitoring System for People at Risk: Methodology and Modeling

Wearable health-monitoring systems (WHMSs) represent the new generation of healthcare by providing real-time unobtrusive monitoring of patients' physiological parameters through the deployment of several on-body and even intrabody biosensors. Although several technological issues regarding WHMS still need to be resolved in order to become more applicable in real-life scenarios, it is expected that continuous ambulatory monitoring of vital signs will enable proactive personal health management and better treatment of patients suffering from chronic diseases, of the elderly population, and of emergency situations. In this paper, we present a physiological data fusion model for multisensor WHMS called Prognosis. The proposed methodology is based on a fuzzy regular language for the generation of the prognoses of the health conditions of the patient, whereby the current state of the corresponding fuzzy finite-state machine signifies the current estimated health state and context of the patient. The operation of the proposed scheme is explained via detailed examples in hypothetical scenarios. Finally, a stochastic Petri net model of the human-device interaction is presented, which illustrates how additional health status feedback can be obtained from the WHMS' user.

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 regular languages over finite and infinite words

We consider finite automata over semirings and quemirings accepting finite and infinite words, respectively. We obtain Kleene theorems for fuzzy languages consisting of finite and infinite words. Furthermore, we introduce regular fuzzy grammars and linear fuzzy systems and we show that both of them specify the class of recognizable fuzzy languages consisting of finite and infinite words.

Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks

There has been an increased interest in combining fuzzy systems with neural networks because fuzzy neural systems merge the advantages of both paradigms. On the one hand, parameters in fuzzy systems have clear physical meanings and rule-based and linguistic information can be incorporated into adaptive fuzzy systems in a systematic way. On the other hand, there exist powerful algorithms for training various neural network models. However, most of the proposed combined architectures are only able to process static input-output relationships; they are not able to process temporal input sequences of arbitrary length. Fuzzy finite-state automats (FFAs) can model dynamical processes whose current state depends on the current input and previous states. Unlike in the case of deterministic finite-state automats (DFAs), FFAs are not in one particular state, rather each state is occupied to some degree defined by a membership function. Based on previous work on encoding DFAs in discrete-time second-order recurrent neural networks, we propose an algorithm that constructs an augmented recurrent neural network that encodes a FFA and recognizes a given fuzzy regular language with arbitrary accuracy. We then empirically verify the encoding methodology by correct string recognition of randomly generated FFAs. In particular, we examine how the networks' performance varies as a function of synaptic weight strengths.

On fuzzy regular languages

We introduce the concept of a max-min fuzzy language, FL ν ( M), and a min-max fuzzy language, FL ⋏(M) , recognized by a type of fuzzy automaton M. We show that if L 1 and L 2 are finite-valued F ν -regular languages, then so are L 1 ∪ L 2 and L 1 ∩ L 2. We give a form of a fuzzified pumping lemma which we use to give a necessary and sufficient condition for FL ν ( M) to be nonconstant.

Fuzzy language on free monoid

In this paper, we shall introduce the notion of fuzzy regular language, adjunctive language, and dense language, and discuss their algebraic character and algebraic properties.

PROOF OF A FUZZY REGULAR LANGUAGE THEOREM BY USING LEVEL SETS—A NOTE

Fuzzy languages and level sets are defined and illustrated by examples. Properties of level sets are presented. A fuzzy regular language theorem may be proved through the use of the properties of level sets. Level sets offer what appears to be a useful tool in theorem proving in fuzzy languages, pictorial databases, natural language translation and processing, and many others. Through the use of level sets, results obtained in formal languages may be used in fuzzy languages and related areas.

Deterministic Acceptors of Regular Fuzzy Languages

The one-to-one relationship between finite automata, regular (type-3) languages, and regular expressions is well known. This correspondence demonstrates the use of regular expressions for describing deterministically finite fuzzy automata and regular fuzzy languages, and introduces a normal form for the production of a regular fuzzy grammar when the ``max(min)'' rule is used.