In this paper a new cluster validity index is introduced, which assesses the average compactness and separation of fuzzy partitions generated by the fuzzy c-means algorithm. To compare the performance of this new index with a number of known validation indices, the fuzzy partitioning of two data sets was carried out. Our validation performed favorably in all studies, even in those where other v...

Compact fuzzy topological spaces were first introduced by Chang [3]. o-compact fuzzy topological spaces were introduced by Gantner et al. [4]. Abd El-Monsef et al. [1] introduced the notion of e-aimost compact fuzzy topological spaces. Mashhour et al. [8] introduced the notion of bifuzzy topological spaces and defined the notion of o-compactness in those spaces. In this paper, we obtain some ne...

Much research has shown that fuzzy c-means clustering is a powerful tool for partitioning samples into different categories. However, the cost function of the classical fuzzy c-means (FCM) is defined by the distances from data to the cluster centers with their fuzzy memberships. In this study, a new fuzzy clustering algorithm, namely the fuzzy weighted c-means (FWCM), is proposed. In this propo...

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...

Firefly algorithm is a swarm-based algorithm that can be used for solving optimization problems. In this paper, we focus on image clustering algorithm using the fuzzy set of possible solution is incorporated into the original firefly to improve the performance. The movement of the firefly still follows the original pattern but they are updated according fuzzy c-means algorithm. All method, k-me...

This paper describes a method for discovering substructures in data using a fuzzy graph match. A previous implementation of the Subdue system discovers substructures based on the psychologically-motivated criteria of cognitive savings, compactness, connec-tivity and coverage. However, the instances in the data must exactly match the discovered substructures. We describe a new implementation of ...

In this paper we obtain some properties of the weak smooth α-closure and weak smooth α-interior of a fuzzy set in smooth topological spaces and introduce the concepts of several types of weak∗ smooth compactness in smooth topological spaces and investigate some of their properties.

The purpose of this paper is to study soft sets and soft topological spaces. We also introduce the concepts of soft interior point, soft interior, soft neighborhood, soft continuity and soft compactness. The relationships between soft topology and fuzzy topology are also provided. Also, some basic properties of these concepts are explored. 2010 AMS Classification: 06D72, 54A40