On algebraic study of fuzzy automata

Tiwari, S. P.; Yadav, Vijay K.; Singh, Anupam

doi:10.1007/s13042-014-0233-5

Cited by 14 publications

(8 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The required notions of lattices are recalled here from [8,22,58,59] as per the need of the paper. Definition 2.1.…”

Section: Latticesmentioning

confidence: 99%

“…The Zadeh's [12] concept of fuzzy sets to handle vague or imprecise concepts, initially incorporated in classical automata theory by Wee [13], Santos [14], Wee and Fu [15], Santos [16], Lee and Zadeh [17], and Kumbhojkar & Chaudhri [18] to introduce the concept of fuzzy finite state automaton (FFSA) and fuzzy languages. The algebraic views of FFSA have been studied by Mordeson and Malik [19,20] and Jin [21] whereas lattice theoretic aspects of FFSA have been studied in Tiwari, Yadav, and Singh [22]. The computational model rough finite state automaton was introduced by Basu [23] to model systems with insufficient and incomplete data set obtained by real-world applications and is further generalized by Yadav, Tiwari, Mausam and Yadav [24] and shown to have real-world application of model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

Ruhela,

Syropoulos,

Yadav

et al. 2023

Preprint

View full text Add to dashboard Cite

The aim of this work is to broaden the theory of computation by making use of fuzzy sets and multisets, which are generalization of ordinary sets. We study fuzzy multiset finite automata (FMFA), which are characterized by the incorporation of vagueness when it comes to the choice of the next state and multiple occurrences of the same input symbol. The resulting automaton is a genaralization of both classical automata and fuzzy automata. We discuss the algebraic characteristics of FMFA sub-automata—separatedness, strongly connectedness, cyclic, directable, and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on state set of FMFA. Intrestingly, for a given FMFA, a new FMFA can be constructed that is a homomorphic image of the original FMFA. We define different posets structures that can be associated with a given FMFA and show that some of them are upper semilattices and discuss the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a posets/FUSL associated with a given FMFA. Finally, we introduce the concept of decomposition of a FMFA in two different ways and characterize the strongly connected, triangular and directable FMFA.

show abstract

“…The required notions of lattices are recalled here from [8,22,58,59] as per the need of the paper. Definition 2.1.…”

Section: Latticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

Ruhela,

Syropoulos,

Yadav

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…These days, Galois connections appear ubiquitary to play a vital role in human reasoning involving hierarchies. For example, some of its applications area covering situations or systems having (i) precise natures are; formal concept analysis (cf., Belohalavek and Konecny [7], Ganter and Wille [12], Wille [35]), category theory (cf., Herrlich and Husek [15], Kerkhoff [21]), logic (cf., Cornejo et al, [9]), category theory, topology and logic (cf., Denecke et al, (Eds) [10]); (ii) imprecise or uncertain natures are; mathematical morphology, category theory (cf., García et al, [14]), fuzzy transform (cf., Perfilieva [27]), Soft computing (cf., García-Pardo et al, [13]); and (iii) vagueness natures; data analysis, reasoning having incomplete information (cf., Järvinen [19]), Pawlak [26], Perfilieva [27]). Here, it is important to note that the equivalence relations based on original Pawlak's (cf., Pawlak [26]), approximation operators form isotone Galois connections and turn out to be interior and closure operators.…”

Section: Introductionmentioning

confidence: 99%

An algebraic study of LB-valued general fuzzy automata: On the concept of the layers

Abolpour,

Shamsizadeh

2023

JAHLA

View full text Add to dashboard Cite

The present study aims at introducing a new concept of layer of LB-valued general fuzzy automata (LB-valued GFA) where B is regarded as a set of propositions about the GFA, in which its underlying structure has been a lattice-ordered monoid. In general, it demonstrates that the layer plays a key role in the algebraic study of LB-valued GFA by characterizing the concepts of subautomata and separated subautomata of an LB-valued GFA in terms of its layers. In other words, it highlights that every LB-valued general fuzzy automaton has at least one strongly connected subautomaton. In specific, the characterization of some algebraic concepts such as subautomaton, retrievability and connectivity of an LB-valued GFA in terms of its layers is provided. In addition, it is shown that the maximal layer of a cyclic LB-valued general fuzzy automaton and minimal layer of a directable LB-valued general fuzzy automaton are unique. Finally, we investigate the different poset structures associated with an LB-valued general fuzzy automaton, demonstrating some of these posets as finite upper semilattice, and introducing the isotone Galois connections between some of the pairs of the posets/finite upper semilattices introduced.

show abstract

“…After that, multidirectional research in the area of fuzzy automata and languages is reported in the literature. The algebraic aspects of fuzzy automata and languages have been studied in [32,51]. The minimal realization problem of fuzzy languages has been studied algebraically in [21], by category-theoretic approach in [50,53,55], and in bicategory theoretic setting in [52,54,63] to brings closer the gap between classical automata theory and natural languages.…”

Section: Introductionmentioning

confidence: 99%

Generalized rough and fuzzy rough automata for semantic computing

Yadav

Tiwari

Kumari

et al. 2022

Int. J. Mach. Learn. & Cyber.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

On algebraic study of fuzzy automata

Cited by 14 publications

References 21 publications

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

An algebraic study of LB-valued general fuzzy automata: On the concept of the layers

Generalized rough and fuzzy rough automata for semantic computing

Contact Info

Product

Resources

About