L-Fuzzy Multiset Recognizer: Determinization and Minimization

This research aims to investigate the determinization andminimization 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-LMR over a quantale L. We, then characterize introduced L-LMR with a multiset regular language (MRL). Next, we investigate the method of construction of a complete L-FMR from a given incomplete L-FMR, and show that if K(R) is the MRL recognized by an incomplete L-FMR R, then there is a completionRc ofRsuch thatK(R) = K(Rc). Moreover, we also illustrate these notions with examples. Further, we introduce a newmethod for the construction of an equivalent deterministicL-fuzzy multiset recognizer (DLMR) fromagivenL-fuzzy multiset recognizer viaL-fuzzy subsets and accessibleL-fuzzy subset construction. Furthermore, we characterize introduced DLMR with an L-fuzzy multiset regular languages (L-FMRL). In the last, we introduce the concepts related to minimal DLMR and then we obtain a minimal DLMR for a given L-FMRL.

Automated summary

This research investigates the determinization and minimization problems of a new class of fuzzy recognizers with input as multisets. It introduces and examines the concepts of L-fuzzy multiset recognizers (LLMRs) and characterizes them with multiset regular languages (MRLs). It also proposes a method for constructing an equivalent deterministic L-fuzzy multiset recognizer (DLMR) from a given LLMR using fuzzy subsets and accessible fuzzy subset construction.