FCM-type cluster validation is a technique for searching for the optimal fuzzy partition, in which the number of clusters is evaluated by considering the degree of overlapping of fuzzy memberships, cluster compactness or cluster separation. In this paper, a new approach for FCM-type cluster validation in fuzzy co-clustering is proposed. Because fuzzy co-clustering does not use cluster prototype...

Given a nonempty set X, a fuzzy ideal I on X is a collection of subsets of X closed under finite union and subset operations. In this paper we define a space to be locally I fuzzy compact space if every point in the space has an I fuzzy compact neighbourhood. Basic results concerning locally I fuzzy compact spaces are given relating to subspaces, preservation of functions, and products. Classic...

Abstract. A new form of α-compactness is introduced in L-topological spaces by α-open L-sets and their inequality where L is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice L. It can also be characterized by means of α-closed L-sets and their inequality. When L is a completely distributive de Morgan algebra, its many characterizations are presented and the re...

In this paper, the well-known Egoroff’s theorem in classical measure theory is established on Sugeno fuzzy measure spaces. Taylor’s theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff’s theorem is obtaine...

The notion of validation set of a formula in a fuzzy logic was introduced by Butnariu, Klement and Zafrany. It is the set of all evaluations of the formula for all possible evaluations of its atomic symbols. We generalize this notion to sets of formulas. This enables us to formulate and prove generalized theorems on satissability and compactness of various fuzzy logics. We also propose and stud...

In this paper we introduce stronger form of the notion of cover so-called p-cover which is more appropriate. According to this cover we introduce and study another type of compactness in L-fuzzy topology so-called C*-compact and study some of its properties with some interrelation.

In an L-topological space we present good definitions for local compactness, weak local compactness and relative local compactness. We obtain the equivalence of these properties in a Hausdorff space and we also obtain a one point compactification theorem.

In this paper we introduce a definition of gradation of continuity ingraded fuzzy topological spaces and study its various characteristic properties.The impact of the grade of continuity of mappings over the N-compactnessgrade is examined. Concept of gradation is also introduced in openness, closed-ness, homeomorphic properties of mappings and T2 separation axiom. Effectof the grades interrelat...

In this paper, a novel modified evolutionary fuzzy clustering has been proposed. This technique exploits parameters such as Minkowski distance, Xie Beni index, and classification entropy. These parameters turn to account to polish the performance measure by incorporating shape of the cluster, class compactness and partitioning quality respectively in standard Fuzzy C-Means clustering. Moreover,...