Fuzzy Linear Languages
Formal languages, linear languages, linear automata, fuzzy languages, fuzzy automata.
The formal languages were introduced in the late 50's, and from then it have been of a great importance in computer science, especially for applications in lexical analysis and syntactic necessary during the development of compilers and also in grammatical inference techniques. The extended Chomsky hierarchy, relates the mains classes of formal languages in term of their reach. In addition, also is possible stablish a relationship between the classes of the formal languages in the Chomsky hierarchy and formalisms such as state machines (or automata) and grammars. Among the languages classes in this hierarchy, the linear languages class have at least four types of "devices" (state machines) characterizing or representing them. Among them are the non-deterministic linear λ-automata proposed by Bedregal. At the end of the 60s, Lee and Zadeh proposed the fuzzy languages in an attempt to bridge the gap between formal and natural languages. In turn, Wee Fu in order to capture the notion of uncertainty during the process recognition of string of a language, introduces the concept of fuzzy automata. As in classical theory, we can trace a relationship between the classes of fuzzy languages and fuzzy automata. However, different from the classical theory, until now, there is no fuzzy automata model directly to compute just on the class the fuzzy linear languages, i.e. that relates to the fuzzy linear languages directly. Therefore, this work proposes to conduct a study on a fuzzy automata model, based on the non-deterministic linear λ-automata, which recognize the fuzzy linear languages. Besides that, as in the study of formal languages, the investigation on closure property of some operators on language classes is an important point, in this work we will also investigate which of the fuzzy operators (union, intersection, etc.) that are closed on the classes of fuzzy linear languages.