(EUSFLAT, 2001) Astrain Escola, José Javier; Villadangos Alonso, Jesús; González de Mendívil Moreno, José Ramón; Garitagoitia Padrones, José Ramón; Fariña Figueredo, Federico; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Automática y Computación; Automatika eta Konputazioa
In this paper, we introduce a fuzzy
automaton for computing the similarity
between pairs of strings and a genetic
method for adjusting its parameters.
The fuzzy automaton models the
edit operations needed to transform any
string into another one. The selection of
appropriate fuzzy operations and fuzzy
membership values for the transitions
leads to improve the system performance
for a particular application.
(Elsevier, 2024-11-01) González de Mendívil Grau, Aitor; Fariña Figueredo, Federico; Stanimirovic, Stefan; Micic, Ivana; González de Mendívil Moreno, José Ramón; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Designing automata minimization algorithms is a significant topic in Automata Theory and Languages with practical applications. In this paper, we develop an efficient minimization algorithm for deterministic fuzzy finite automata over locally finite lattices. More precisely, the algorithm outputs an equivalent minimal crisp-deterministic fuzzy finite automaton for an input fuzzy deterministic finite automaton (FDfA). The running time of the proposed algorithm is polynomial for particular types of locally finite lattices, specifically for max-min-based complete residuated lattices. The intuition behind the proposed algorithm relies on the polynomial minimization algorithm's intuition for ordinary deterministic automata developed by Vazquez de Parga, Garcia, and Lopez (2013) [35]. The motivation for this study comes from the fact that the original algorithm's notions and meanings are lost in the context of fuzzy automata. Thus, we establish a new theoretical foundation that provides the correctness and the polynomial-time nature of this new crisp-minimization algorithm for FDfAs.
