L-Fuzzy Multiset Recognizer: Determinization and Minimization - Mallika Dhingra, Mallika Dhingra; Mahesh Kumar Dubey, Mahesh Kumar Dubey; Jacob Kavikumar, Jacob Kavikumar (IEEE, 2023)
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-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 completion Rc of R such that K(R) = K(Rc). 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 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.