Sophisticated fuzzy rule systems are supposed to be flexible, complete, consistent and compact (FC(3)). Flexibility, and consistency are essential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the number of the input variables increases. However, the completeness and consistency conditions are often violated if a fu...

The convergence theory not only is an significantly basic theory of fuzzy topology and fuzzy analysis but also has wide applications in fuzzy inference and some other aspects. In this paper, we introduce the concept of α-generalized-remoteneighborhood of fuzzy points and establish the Moore-Smith α-generalized-convergence theory of L-fuzzy nets. Then, we introduce and study the concept of L-fuz...

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

Aiming at improving the well-known fuzzy compactness and separation algorithm (FCS), this paper proposes a new clustering algorithm based on feature weighting fuzzy compactness and separation (WFCS). In view of the contribution of features to clustering, the proposed algorithm introduces the feature weighting into the objective function. We first formulate the membership and feature weighting, ...

we present some model theoretic results for {l}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by chang and keisler.we prove compactness theorem with respect to the class of allstructures taking values in the {l}ukasiewicz $texttt{bl}$-algebra.we also prove some appropriate preservation theorems concerning universal and inductive theories.finally, skolemizatio...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

In [3] and [6] the concepts of smooth closure, smooth interior, smooth α-closure and smooth α-interior of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth α-compactness in terms of these concepts introduced in [3] and [6] and investigate some of their properties.