On fuzzy multiset regular languages

Sharma, Brajesh Kumar; Gautam, Vinay; Tiwari, S. P.; Bhattacherjee, Vandana

doi:10.5899/2017/jfsva-00340

Cited by 8 publications

(8 citation statements)

References 30 publications

(39 reference statements)

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“…Ciobanu [34] studied Mealy multiset automata, Kudlek, Totzke and Zetzsche [35] studied multiset pushdown automata and multiset languages and Kudlek and Mitrana [36] studied closure properties of multiset language families. To incorporate vagueness or uncertainty in multiset automata and their languages, the concept of fuzzy multiset regular grammar (FMRG), FMFA and their languages were introduced and studied by Wang, Yin and Gu [37], Martinek [38,39] studied determinism and minimization of FMFA, Sharma, Tiwari and Sharan [40] studied the transformation semigroup and covering of a FMFA, Tiwari, Gautam and Dubey [41] studied fuzzy multiset languages (FMLs) whereas Sharma, Syropoulos and Tiwari [42] studied FMRG. It is worth to mention here that the multiset automata and fuzzy multiset automata are generalized versions of classical and fuzzy automata whose inputs are multisets (bags), in these models of computations processing of a symbol does not follow any strict order, i.e., any symbol from'input bag' can be utilized without affecting the output.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

Ruhela,

Syropoulos,

Yadav

et al. 2023

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

Ruhela,

Syropoulos,

Yadav

et al. 2023

Preprint

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“…The most notable examples are the GAMMA model [6,7], the chemical abstract machine [8], and P systems [9]. Similarly, there are models of computation whose core elements are fuzzy multisets [5,10] (but see also the 5th chapter of [11]).…”

Section: Introductionmentioning

confidence: 99%

On Triangular Multisets and Triangular Fuzzy Multisets

Syropoulos¹

2022

Mathematics

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The basic set operations between fuzzy sets are defined using the min and max functions; however, later on, new operators were introduced that used other functions, which, nevertheless, had similar properties to functions min and max. The resulting fuzzy set theories are more suitable for the description and processing of specific data sets. Crisp and fuzzy multisets have found numerous applications but still the basic operations are based on functions min and max. It is straightforward to replace these functions in the fuzzy part of fuzzy multisets; however, it is not as easy but is feasible to do the same with the multisets and the “crisp” part of fuzzy multisets. The new mathematical structures are called triangular multisets and triangular fuzzy multisets, respectively. The aim is to facilitate the processing of certain data sets so they can be used in multi-criteria decision making and computing.

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“…e recent contribution to the study of fuzzy multiset automata and fuzzy multiset languages is due to Sharma et al [76,77], Wang and Li [64], Pal and Tiwari [78], and Tiwari et al [79].…”

Section: Introductionmentioning

confidence: 99%

“…e authors in [76], studied algebraic aspects of fuzzy multiset automata like fuzzy multiset transformation semigroup and coverings of fuzzy multiset finite automata, while authors in [77] studied fuzzy multiset regular languages and proved pumping lemma and use it to point out mandatory condition for fuzzy multiset languages being non-constant. In [64], the method of transformation of lattice valued nondeterministic multiset automata into deterministic lattice valued multiset automata (DLMA), and then its minimization algorithm; some lattice-valued regular multiset languages accepted by some special minimal DLMA the lattice-valued regular multiset language decomposition by some simple were studied with structure for truth values of a fuzzy set as distributive lattices.…”

Section: Introductionmentioning

confidence: 99%

A General Categorical Framework of Minimal Realization Theory for a Fuzzy Multiset Language

Yadav

Tiwari

2022

Mathematical Problems in Engineering

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This paper is to study the minimal realization theory for a fuzzy multiset language in the framework of category theory, which has already provided the tools and techniques for the advancement of several features of theoretical computer science. Specifically, by using the well-known categorical concepts, it is shown herein that there is a minimal realization (called the Nerode realization) for each fuzzy multiset language, and all minimal realizations for a given fuzzy multiset language are isomorphic to it.

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On fuzzy multiset regular languages

Cited by 8 publications

References 30 publications

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

On Triangular Multisets and Triangular Fuzzy Multisets

A General Categorical Framework of Minimal Realization Theory for a Fuzzy Multiset Language

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