The reticulation of an algebra was first defined for commutative rings by Simmons [19] and it was extended by Belluce to non-commutative rings [3]. As for the algebras of fuzzy logics, Belluce also constructed the reticulation of an MV-algebra [2], G. Georgescu defined the reticulation of a quantale [8] and L. Leuştean made this construction for BL-algebras [13, 14]. In each of the papers cited...

Pseudo-BL algebras and pseudo-effect algebras arose in two rather different fields: fuzzy logics and quantum logics. In this paper, by introducing the notion of pseudo-weak MV-effect algebra which is non-commutative generalization of weak MV-effect algebra, we investigate the mutual relationship between pseudo-BL algebras and pseudo-effect algebras. We prove that dual pseudo-BL algebra under ce...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

Traditional Fuzzy Automata are not sufficient to model complex real life applications such as biomedical systems where the inputs can be in terms of Fuzzy. Watson Crick Finite Automaton, which works on Double Stranded tapes was introduced a computational analyze DNA molecule for purpose. The concept Fuzziness and studied theory Automaton. thought an effective computing with problems having inco...

Positions and derivatives are two essential notions in the conversion methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regular expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction generalizes the notion of position making it compatible wit...

We show that if a Lie group acts properly on a co-oriented contact manifold preserving the contact structure then the contact quotient is topologically a stratified space (in the sense that a neighborhood of a point in the quotient is a product of a disk with a cone on a stratified space). As a corollary we obtain that symplectic quotients for proper Hamiltonian actions are topologically strati...

As Granular Computing has gained interest, more research has lead into using different representations for Information Granules, i.e., rough sets, intervals, quotient space, fuzzy sets; where each representation offers different approaches to information granulation. These different representations have given more flexibility to what information granulation can achieve. In this overview paper, ...

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...