On Quotient Structures of Fuzzy Multiset Finite Automata

Abstract

The objective of this paper is to characterize the quotient structures of fuzzy multiset finite automata. We introduce different congruence relation on multiset associated with fuzzy multiset finite automata and show that each congruence relation associates a semigroup with the fuzzy multiset finite automata. We also discuss the charaterization of fuzzy multiset finite automata by defining an admissible relation.

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

“…In case of FMFA, algebraic concepts such as transformation semi-group and covering of FMFA have been studied by Sharma, Tiwari and Sharan [40]. Recently, Singh, Dubey and Perfilieva [45], introduced several congruence relations on multiset associated with FMFA and demonstrate that each of these congruence relations associates a semigroup with FMFA. In [45], an admissible relation on a FMFA has been defined to characterize the FMFA, and it was shown there that there exists an isomorphism between FMFA and the quotient structures on another FMFA.…”

“…Recently, Singh, Dubey and Perfilieva [45], introduced several congruence relations on multiset associated with FMFA and demonstrate that each of these congruence relations associates a semigroup with FMFA. In [45], an admissible relation on a FMFA has been defined to characterize the FMFA, and it was shown there that there exists an isomorphism between FMFA and the quotient structures on another FMFA. In this paper, we enrich the algebraic theory of FMFA by characterization of some algebraic concepts of FMFA, which are still not studied as mentioned in item (ii) above.…”

“…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. Furthermore, Wang and Li [43] studied the lattice-valued FMFA minimization problem and Pal and Tiwari [44] considered Brazozowaski's algorithm and the categorical approaches for the same, while Singh, Dubey and Perfilieva [45] discussed quotient structures of FMFA, and Gautam [46] studied l-valued FMFA and l-valued FMLs. Recently Yadav and Tiwari [47] provide a general categorical framework of minimal realization of fuzzy multiset languages.…”

Fault Diagnosis in Regenerative Braking System of Hybrid Electric Vehicles by Using Semigroup of Finite-State Deterministic Fully Intuitionistic Fuzzy Automata

“…Fuzzy automata are used to handle system uncertainties more accurately, whereas classical automata fail to cater to the circumstances. Fuzzy automata have been frequently employed since the introduction of fuzzy technology and neural networks [3][4][5][6][7][8][9][10][11][12][13]. Furthermore, there were a variety of problems to be resolved, for example, medical diagnosis, car anti-crash radar, freeway management, urban road traffic control, and obstacle recognition in front of a vehicle, which required flexible, quick, and accurate decisions, and then, fuzzy neural network automata (FNNA) [14][15][16][17] are an excellent choice.…”