scholarly journals Soft ditopological spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 209-222 ◽  
Author(s):  
Tugbahan Dizman ◽  
Alexander Sostak ◽  
Saziye Yuksel
Keyword(s):  
Fuzzy Sets ◽  
Soft Set ◽  
Fuzzy Topology ◽  
Basic Properties ◽  
Soft Topology ◽  
Continuous Mappings ◽  
Basic Concepts

We introduce the concept of a soft ditopological space as the "soft Generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Ert?rk, ?. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 171-199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.

scholarly journals Infra Soft Semiopen Sets and Infra Soft Semicontinuity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tareq M. Al-shami ◽  
A. A. Azzam
Keyword(s):  
Soft Set ◽  
Finite Product ◽  
Finite Intersection ◽  
Soft Topology ◽  
Continuous Mappings

To contribute to the area of infra soft topology, we introduce one of the generalizations of infra soft open sets called infra soft semiopen sets. We establish some characterizations of them and study their main properties. We determine under what condition this class is closed under finite intersection and show that this class is preserved under infra soft continuous mappings and finite product of soft spaces. Then, we present the concepts of infra semi-interior, infra semiclosure, infra semilimit, and infra semiboundary soft points of a soft set and elucidate the relationships between them. Finally, we exploit infra soft semiopen and infra soft semiclosed sets to define new types of soft mappings. We characterize each one of these soft mappings and explore main features.

scholarly journals Neutrosophic soft δ-topology and neutrosophic soft δ-compactness

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3441-3458
Author(s):  
Ahu Acikgoz ◽  
Ferhat Esenbel
Keyword(s):  
Basic Properties ◽  
Soft Topology ◽  
Open Set ◽  
Continuous Mappings ◽  
Regular Open

We introduce the concepts of neutrosophic soft ?-interior, neutrosophic soft quasi-coincidence, neutrosophic soft q-neighbourhood, neutrosophic soft regular open set, neutrosophic soft ?-closure, neutrosophic soft ?-closure and neutrosophic soft semi open set. It is also shown that the set of all neutrosophic soft ?-open sets is a neutrosophic soft topology, which is called the neutrosophic soft ?-topology. We obtain equivalent forms of neutrosophic soft ?-continuity. Moreover, the notions of neutrosophic soft ?-compactness and neutrosophic soft locally ?-compactness are defined and their basic properties under neutrosophic soft ?-continuous mappings are investigated.

scholarly journals New Soft Structure: Infra Soft Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Closure Operators ◽  
Relative Topology ◽  
Closed Sets ◽  
Soft Topology ◽  
Soft Limit ◽  
Basic Concepts ◽  
Soft Topological Space

It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

scholarly journals Fuzzy soft metric and fuzzifying soft topology induced by fuzzy soft metric

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 645-653
Author(s):  
Abdülkadir Aygünoğlu ◽  
Ebru Aydoğdu ◽  
Halis Aygün
Keyword(s):  
Set Theory ◽  
Metric Spaces ◽  
Soft Set ◽  
Topological Structures ◽  
Basic Properties ◽  
Soft Topology

Our main goal with this paper is to construct soft topology and fuzzifying soft topology induced by fuzzy soft metric. For this, we present fuzzy soft metric spaces compatible to soft set theory and studied some of its basic properties. Then we investigate soft topological structures induced by fuzzy soft metrics.

scholarly journals Cartesian product and Topology On Fuzzy BI-Algebras

2021 ◽  
Vol 8 ◽  
pp. 29-33
Author(s):  
Gerima Tefera ◽  
Abdi Oli
Keyword(s):  
Cartesian Product ◽  
Fuzzy Topology ◽  
Basic Properties ◽  
And Topology

In this paper,the concepts of homomorphism in fuzzy BI-algebra is intro- duced, and also basic properties of homo- morphisms are investigated. The cartesian product in fuzzy ideals of BI-algebra is investigated with related prop- erties; The concepts of fuzzy topology on BI- algebra elaborated.

scholarly journals Fuzzy Soft Multiset Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Soft Set ◽  
Mathematical Tool ◽  
Basic Properties ◽  
Definition Of

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown.

Connectedness Between Soft Sets

2018 ◽  
Vol 14 (01) ◽  
pp. 53-71 ◽  
Author(s):  
Samajh Singh Thakur ◽  
Alpa Singh Rajput
Keyword(s):  
Soft Set ◽  
Topological Spaces ◽  
Soft Sets ◽  
Continuous Mappings ◽  
Weakly Continuous

In the present paper, the concepts of soft connectedness between soft sets, soft set-connected and soft weakly continuous mappings in soft topological spaces have been introduced and studied.

Some results on fuzzy topology on fuzzy sets

1993 ◽  
Vol 56 (3) ◽  
pp. 331-336 ◽  
Author(s):  
A.K. Chaudhuri ◽  
P. Das
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Topology

scholarly journals Fuzzy Normed Rings

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 515 ◽  
Author(s):  
Aykut Emniyet ◽  
Memet Şahin
Keyword(s):  
Prime Ideal ◽  
Fuzzy Sets ◽  
Maximal Ideal ◽  
Ring Homomorphism ◽  
Ring Theory ◽  
Basic Properties ◽  
Normed Ring ◽  
Normed Ideal ◽  
Algebraic Properties ◽  
Definition Of

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy normed ring homomorphism, fuzzy normed subring, fuzzy normed ideal, fuzzy normed prime ideal, and fuzzy normed maximal ideal of a normed ring, respectively. We show some algebraic properties of normed ring theory on fuzzy sets, prove theorems, and give relevant examples.

scholarly journals Multiaspect Soft Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Nor Hashimah Sulaiman ◽  
Daud Mohamad
Keyword(s):  
Soft Set ◽  
Soft Sets ◽  
Basic Concepts ◽  
Novel Concept

We introduce a novel concept of multiaspect soft set which is an extension of the ordinary soft set by Molodtsov. Some basic concepts, operations, and properties of the multiaspect soft sets are studied. We also define a mapping on multiaspect soft classes and investigate several properties related to the images and preimages of multiaspect soft sets.

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