$L$-Fuzzy Multiset Recognizer: Determinization and Minimization
Mallika Dhingra, M. K. Dubey, Kavikumar Jacob · IEEE Transactions on Emerging Topics in Computational Intelligence · 2022
This research aims to investigate the determinization and minimization problems of a new class of fuzzy recognizers with input as multisets. We begin by introducing and examining the concepts of an$L$-fuzzy multiset recognizer ($L$-LMR), complete, accessible, and coaccessible$L$-LMRover a quantale$L$. We, then characterize introduced$L$-LMRwith a multiset regular language (MRL). Next, we investigate the method of construction of a complete$L$-FMRfrom a given incomplete$L$-FMR, and show that if$K(\mathcal {R})$is theMRLrecognized by an incomplete$L$-FMR$\mathcal {R}$, then there is a completion$\mathcal {R}^{c}$of$\mathcal {R}$such that$K(\mathcal {R})=K(\mathcal {R}^{c})$. Moreover, we also illustrate these notions with examples. Further, we introduce a new method for the construction of an equivalent deterministic$L$-fuzzy multiset recognizer (DLMR) from a given$L$-fuzzy multiset recognizer via$L$-fuzzy subsets and accessible$L$-fuzzy subset construction. Furthermore, we characterize introducedDLMRwith an$L$-fuzzy multiset regular languages ($L$-FMRL). In the last, we introduce the concepts related to minimalDLMRand then we obtain a minimalDLMRfor a given$L$-FMRL.