Regular grammars with truth values in lattice-ordered monoid and their languages

Authors:
Li Sheng;Yongming Li
Affiliations:
Institute of Fuzzy Systems, College of Mathematics and Information Science, Shaanxi Normal University, 710062, Xi’an, China;Institute of Fuzzy Systems, College of Mathematics and Information Science, Shaanxi Normal University, 710062, Xi’an, China
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2006

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Abstract

In this study, we introduce the concept of lattice-valued regular grammars. Such grammars have become a necessary tool for the analysis of fuzzy finite automata. The relationship between lattice-valued finite automata (LA) and lattice-valued regular grammars (LRG) are discussed and we get the following results, for a given LRG, there exists an LA such that they accept the same languages, and vice versa. We also show the equivalence between deterministic lattice-valued regular grammars and deterministic lattice-valued finite automata.