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Fuzzy logic was introduced by Zadeh in 1965. Since then, the importance of fuzzy logic has come increasingly to the present.There are many applications of fuzzy logic in the field of science and engineering, e.g. population dynamics…

Functional Analysis · Mathematics 2011-12-15 Vatan Karakaya , Necip Şimşek , Müzeyyen Ertürk , Faik Gürsoy

Fuzzy anti-norm and corresponding $\alpha$-norms are defined. A few properties of finite dimensional fuzzy anti-normed linear space are studied. Fuzzy $\alpha$-anti-convergence and fuzzy $\alpha$-anti-complete linear space are defined and a…

General Mathematics · Mathematics 2012-02-21 Bivas Dinda , T. K. Samanta , Iqbal H. Jebril

This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft…

General Mathematics · Mathematics 2016-10-06 İsmet Altıntaş , Kemal Taşköprü

Tanay and Kandemir <cite>TK</cite> introduced the topological structure of fuzzy soft sets. In 2013, Manatha and Das <cite>md</cite> defined seperation axioms on fuzzy soft topological spaces. In this paper, we generalized form of the…

General Mathematics · Mathematics 2018-03-28 Serkan Atmaca

In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure, interior and neighbourhood are introduced here and established some important…

General Mathematics · Mathematics 2017-06-06 Manash Jyoti Borah , Bipan Hazarika

In this paper, we introduce a novel fuzzy structure named "fuzzy primal". We study the essential properties and discuss basic operations on it. A fuzzy operator (.)$^\diamond$ on the family of all fuzzy sets is introduced here by applying…

General Topology · Mathematics 2023-08-15 Zanyar A. Ameen , Ramadhan A. Mohammed , Tareq M. Al-shami , Baravan A. Asaad

In this paper, we present the concept of relations in intuitionistic fuzzy soft set and study some of their properties and also discuss symmetric, transitive and reflexive intuitionistic fuzzy soft relations.

General Mathematics · Mathematics 2012-02-22 Bivas Dinda , T. K. Samanta

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets.…

General Mathematics · Mathematics 2015-06-11 J. Mahanta , P. K. Das

Given a nonempty set $X$ and a function $f:X \rightarrow X$, three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.

General Mathematics · Mathematics 2017-02-07 Ismael Akray

Molodstov[10] introduced soft set theory as a new mathematical approach for solving problems having uncertainties. Many researchers worked on the findings of structures of soft set theory and applied to many problems having uncertainties.…

General Mathematics · Mathematics 2014-09-12 Sabir Hussain

The concept of interval-valued fuzzy soft $\beta$-covering approximation spaces (IFS$\beta$CASs) is introduced to combine the theories of soft sets, rough sets and interval-valued fuzzy sets, and some fundamental propositions concerning…

General Mathematics · Mathematics 2024-04-12 Shizhan Lu

In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets…

Logic · Mathematics 2016-02-12 Irfan Deli , Naim Çağman

Molodtsov \cite{molodtsov-1999} proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Sabir and Naz \cite{shabir-2013} defined notion of bipolar soft…

General Mathematics · Mathematics 2016-01-21 Faruk Karaaslan , Serkan Karataş

In this paper, we present the fuzzy monoids and vague monoids by using aggregation operators. The unit interval with a $t$-norm or a $t$-conorm is a special monoid, so we mainly talk about fuzzy subsets of monoids. Firstly, the…

General Mathematics · Mathematics 2022-05-23 Wei Li , Haohao Wang , Yuanhao Liu , Bin Yang

A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded…

General Mathematics · Mathematics 2017-04-27 Purbita Jana , Mihir K. Chakraborty

The main aim of this paper is to introduced the operations "Union" and "Intersection," and four operators $O_1, O_2, O_3, O_4 $ on interval-valued hesitant fuzzy soft sets and discuss some of their properties.

General Mathematics · Mathematics 2016-04-05 Manash Jyoti Borah , Bipan Hazarika

Fuzzy numbers are commonly represented with fuzzy sets. Their objective is to better represent imprecise data. However, operations on fuzzy numbers are not as straightforward as maths on crisp numbers. Commonly, the Zadeh's extension rule…

Artificial Intelligence · Computer Science 2025-10-27 Krzysztof Siminski

The major part of this thesis deals with fuzzy geometric logic and fuzzy geometric logic with graded consequence. The first chapter mainly contains the concept of topological system introduced by S. Vickers in 1989. In Chapter 2 the notion…

General Mathematics · Mathematics 2017-05-16 Purbita Jana

In this paper, we introduce soft continuous mappings which are defined over an initial universe set with a fixed set of parameters. Later we study soft open and soft closed mappings, soft homeomorphism and investigate some properties of…

General Mathematics · Mathematics 2016-08-11 Cigdem Gunduz Aras , Ayse Sonmez , Hüseyin Çakallı

The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental…

General Topology · Mathematics 2023-10-24 Zanyar A. Ameen , Samer Al Ghour