A New Classification of Lattice Finite Automata and Their Minimizations Based on L-Fuzzy Strings
Inspired by Li and Pedrycz's work on automata theory based on lattice-ordered monoid, several fuzzy automatons are extended to be lattice finite automatons with membership values in lattice-ordered monoids, and a new classification of lattice finite automata (or LFA, for short) according to their function is advanced in this paper. Then the equivalence or affiliation of them in the same kind is proved. Motivated by the importance of computing with words, we put forward two kinds of generalized LFA whose inputs are instead L-fuzzy strings of the input alphabet. For generalized Mizumoto LFA, we translate it into its canonical LFA with single initial state and deterministic transition function, establish that the canonical LFA is equivalent to the original LFA, and present an algorithm to minimize the canonical LFA. On the other hand, the behavior matrix of the generalized complete Mealy LFA is well defined, and the definition of statewise equivalent relations is presented. Finally, its minimization algorithm is also given based on a finite lattice-ordered monoid.
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Document Type: Research Article
Publication date: September 1, 2013
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