The concept of an M-approximative system is introduced. Basic properties of the category of M-approximative systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximative systems. Keywords— Approximative operator...

This paper is a survey of fuzzy set theory applied in cluster analysis. These fuzzy clustering algorithms have been widely studied and applied in a variety of substantive areas. They also become the major techniques in cluster analysis. In this paper, we give a survey of fuzzy clustering in three categories. The first category is the fuzzy clustering based on fuzzy relation. The second one is t...

The main aim of this paper is to give a characterization of the category of fuzzy soft topological spaces and their continuous mappings, denoted by FSTOP. For this reason, we construct the category of antichain soft topological spaces and their continuous mappings, denoted by ASTOP. Also, we show that the category FSTOP is isomorphic to the category ASTOP.

An L-fuzzy generalization of the so-called Chu correspondences between formal contexts forms a category called L-ChuCors. In this work we show that this category naturally embeds ChuCors, and prove that it is *-autonomous. We also focus on the direct product of two L-fuzzy contexts, which is defined with the help of a binary operation, essentially a disjunction, on a lattice of truth-values L.

Fuzzy ARTMAP (FAM) is currently considered as one of the premier neural network architectures in solving classification problems. One of the limitations of Fuzzy ARTMAP that has been extensively reported in the literature is the category proliferation problem. That is, Fuzzy ARTMAP has the tendency of increasing its network size as it is confronted with more and more data, especially if the dat...

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such...

The Fuzzy Adaptive Resonance Theory (Fuzzy ART) is an unsupervised neural network and allows both binary and continuous input patterns. In this study, we propose a Fuzzy ART Combining Overlapped Categories Using Variable Vigilance Parameters. The vigilance parameters of the proposed method are arranged for every category, and they are varied according to the size of respective categories with l...