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

The goal of this expository paper is to bring forth the basic current elements of soft computing (fuzzy logic, neural networks, genetic algorithms and genetic programming) and the current applications in intelligent control. Fuzzy sets and fuzzy logic and their applications to control systems have been documented. Other elements of soft computing, such as neural networks and genetic algorithms,...

In this paper we associate the three concepts of language, thinking, and meaning with Fuzzy Sets and Systems and Fuzzy Logic. We present some developments in 20 th century history of science and of humanities that show deep links between these concepts and we give a proposal for a fuzzy theoretical interpretation of what is meaning.

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications from a given pair of fuzzy implications. Viewing this as a binary operation ~ on the set I of all fuzzy implications they obtained, for the first time, a monoid structure (I,~) on the set I. Some algebraic aspects of (I,~) had already been explored and hitherto unknown representation results for the Yager’s fa...

This paper is a continuation of the first part of our study on type 〈1, 1〉 fuzzy quantifiers determined by fuzzy measures, in which the basic notions and examples were introduced. Here, we study the properties of permutation invariance and isomorphism invariance of fuzzy quantifiers determined by pairs of functionals (S, φ) and their special cases, e.g., fuzzy quantifiers defined by fuzzy measu...

the main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (brie y soft rgb-closed set) moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g-closed, soft gb-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigat...

The real world has a lot of different aspects which are not usually been specified. In different fields of knowledge like engineering, medical science, mathematics, physics, computer science and artificial intelligence, many problems are simplified by constructing their "models". These models are very complicated and it is impossible to find the exact solutions in many occasions. Therefore, the...

This issue introduces the state-of-art in granular soft computng for pattern recognition and mining and presents some novel ontributions. Granulation is a computing paradigm, among othrs such as self-reproduction, self-organization, functioning of rain, Darwinian evolution, group behavior, cell membranes, and orphogenesis that are abstracted from natural phenomena. Granlation is inherent in hum...

In this paper, we shall give examples to answer that an open problem posed by De Baets et al. in “Triangular norms on product lattices (Fuzzy Sets and Systems 104(1999), 61-75)”.

Since COVID-19 has become a pandemic, education been interrupted in many countries, and training temporarily resumed on online platforms. But it is difficult to determine which of the existing web (or video) conferencing software more suitable for class education. The aim this study sort these platforms according criteria determined by experts select best one among different alternatives using ...