Annals of Communications in Mathematics

Abstract:The purpose of this paper is to introduce and study the notion of various important forms of general type-2 fuzzy grammars, namely, the general type-2 fuzzy grammar in normal form, general type-2 fuzzy linear grammar, general type-2 fuzzy left linear grammar, and general type-2 fuzzy right linear grammar. We establish that each of these forms is equivalent to a general type-2 fuzzy regular grammar (except for an empty string) in the sense that they induce the same class of general type-2 fuzzy languages. These results not only generalizes classical equivalence theorems from fuzzy grammar theory but also provide a theoretical basis for the analysis and future development of general type-2 fuzzy grammar theory.

Abstract:This paper presents a topological approach to the study of rough automata.We introduce the core of a rough automaton and show that it naturally induces a topology on the state set. We show that this topology is preserved under the product of rough automata. We further establish topological characterizations of definite and possible primary subautomata in terms of regular closed sets. Based on these characterizations, we prove primary decomposition theorems for compact rough automata. Overall, this work clarifies the theoretical interplay among rough sets, topology, and automata.