Characterizations of rough finite state automata

Sharan, Shambhu; Srivastava, Arun; Tiwari, S. P.

doi:10.1007/s13042-015-0372-3

Cited by 9 publications

(9 citation statements)

References 26 publications

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“…[ 40 ] (i) For , lower and upper approximations of E in ( U , R ) can be denoted as and , in this case, a rough set in ( U , R ) can be viewed as a pair . (ii) For all , if we denote its equivalence class in ( U , R ) simply by [ u ], then the pair ([ u , [ u ]) is a rough set in ( U , R ) and that .…”

Section: Preliminariesmentioning

confidence: 99%

“…[ 5 , 40 ] The transition map of M can be extended to in the following way: , for all and empty string . For all , , where and …”

Section: Preliminariesmentioning

confidence: 99%

“…[ 3 , 5 , 40 ] Let be a RFSA and be the class of all definable sets in ( Q , R ). Then the block transition map of M can be extended to such that for all : …”

Section: Preliminariesmentioning

confidence: 99%

“…Remark 2.1 [40] (i) For E ⊆ U , lower and upper approximations of E in (U, R) can be denoted as E and E , in this case, a rough set in (U, R) can be viewed as a pair (E, E) . (ii) For all u ∈ U , if we denote its equivalence class…”

Section: Rough Set Fuzzy Set and Fuzzy Rough Setmentioning

confidence: 99%

“…After that, Basu [ 4 ], introduced and studied the concept of rough grammar and rough languages generated by them, whereas the approximation of languages in the rough set was studied in [ 36 ]. The concept of rough finite-state machine introduced by Basu [ 5 ] is further studied by Sharan, Srivastava, and Tiwari [ 40 ] to characterize rough finite state automata, by Tiwari, Sharan and Singh [ 49 ] to discuss coverings of product of rough transformation semigroup, and by Tiwari and Sharan [ 48 ] to introduce the concept of product of rough finite state machine. R. Arulprakasam et al [ 3 ] established a correspondence between rough languages generated by rough grammar and rough languages accepted by rough finite-state automata.…”

Section: Introductionmentioning

confidence: 99%

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Generalized rough and fuzzy rough automata for semantic computing

Yadav

Tiwari

Kumari

et al. 2022

Int. J. Mach. Learn. & Cyber.

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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.

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Section: Preliminariesmentioning

confidence: 99%

“…[ 5 , 40 ] The transition map of M can be extended to in the following way: , for all and empty string . For all , , where and …”

Section: Preliminariesmentioning

confidence: 99%

“…[ 3 , 5 , 40 ] Let be a RFSA and be the class of all definable sets in ( Q , R ). Then the block transition map of M can be extended to such that for all : …”

Section: Preliminariesmentioning

confidence: 99%

Section: Rough Set Fuzzy Set and Fuzzy Rough Setmentioning

confidence: 99%