Li and Pedrycz [Y. M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005) 68–92] have proved fundamental results that provide different equivalentways to represent fuzzy languageswithmembership values in a lattice-orderedmonoid, and generalize the well-known results of the classical theory of fo...

We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show that (i) regular c...

In this paper, we introduce the notions of intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each intuitionistic fuzzy bi-ideal is semiprime and strongly prime. Key words: Intuitionistic fuzzy set; intuitionistic fuzzy bi-ideal; intuitionistic fuzzy prime (resp. strongly prime and semiprime) ...

In this paper we present a different framework for the study of fuzzy finite machines and their fuzzy languages. Unlike the previous work on fuzzy languages, characterized by fuzzification at the level of their acceptors/generators, here we follow a top-down approach by starting our fuzzification with more abstract entities: monoids and particular families in monoids. Moreover, we replace the u...

Many fuzzy automaton models have been introduced in the past. Here, we discuss two basic nite fuzzy automaton models, the Mealy and Moore types, for lexical analysis. We show that there is a remarkable di erence between the two types. We consider that the latter is a suitable model for implementing lexical analysers. Various properties of fuzzy regular languages are reviewed and studied. A fuzz...

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

Based on previous work on encoding deterministic nite-state automata (DFAs) in discrete-time, second-order recurrent neural networks with sigmoidal discriminant functions, we propose an algorithm that constructs an augmented recurrent neural network that encodes fuzzy nite-state automata (FFAs). Given an arbitrary FFA, we apply an algorithm which transforms the FFA into an equivalent determinis...