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Axioms
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Neutrosophic Topology
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Neutrosophic Topology

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 January 2019)

Special Issue Editors

Prof. Dr. Florentin Smarandache

E-Mail Website
Guest Editor
Department of Math and Science, University of New Mexico, 705 Gurley Ave., Gallup Campus, NM 87301, USA
Interests: neutrosophic physics; neutrosophic probability; neutrosophic statistics; neutrosophic algebraic structures; plithogenic set; unmatter; superluminal physics; paradoxism; quantum paradoxes
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Saeid Jafari

E-Mail Website
Guest Editor
College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark
Interests: fuzzy logic and fuzzy topology; neutrosophic theory; general topology; digital topology; topological groups; theory of multifunctions; mathematical aspects of particle physics
Special Issues, Collections and Topics in MDPI journals
Dr. Francisco Gallego Lupiaňez

E-Mail Website
Guest Editor
Department of Mathematics, Universidad Complutense, Ciudad Universitaria, 28040 Madrid, Spain
Interests: topology; covering properties; paracompactness; fuzzy sets; intuitionistic fuzzy sets
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Neutrosophic sets are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. As a consequence topological ideas have been defined and studied on neutrosophic sets, giving birth to Neutrosophic Topology.

Neutrosophic logic, set, probability, statistics, etc., are, respectively, generalizations of fuzzy and intuitionistic fuzzy logic and set, classical and imprecise probability, and classical statistics and so on. For more information see the University of New Mexico website:

http://fs.gallup.unm.edu/neutrosophy.htm

We invite you to contribute papers on neutrosophic topologies and their applications to this Special Issue of the international journal Axioms, which is a Scopus and ESCI journal.

Prof. Dr. Florentin Smarandache
Prof. Dr. Saeid Jafari
Prof. Dr. Francisco Gallego Lupiaňez
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Basic notions and fundamental properties in neutrosophic topological spaces
  • Basic notions and fundamental properties in neutrosophic minimal topological spaces
  • Basic notions and fundamental properties in neutrosophic ideal topological spaces
  • Basic notions and fundamental properties in neutrosophic ideal minimal topological spaces
  • Basic notions and fundamental properties in different types of neutrosophic bitopological spaces
  • Neutrosophic soft sets
  • Neutrosophic rough sets
  • Neutrosophic multifunctions
  • Applications of neutrosophic topologies in various fields

Published Papers (3 papers)

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Research

17 pages, 349 KiB  
Article
Application of Neutrosophic Soft Sets to K-Algebras
by Muhammad Akram, Hina Gulzar, Florentin Smarandache and Said Broumi
Axioms 2018, 7(4), 83; https://doi.org/10.3390/axioms7040083 - 12 Nov 2018
Cited by 3 | Viewed by 2750
Abstract
Neutrosophic sets and soft sets are two different mathematical tools for representing vagueness and uncertainty. We apply these models in combination to study vagueness and uncertainty in K-algebras. We introduce the notion of single-valued neutrosophic soft (SNS) K-algebras and investigate some [...] Read more.
Neutrosophic sets and soft sets are two different mathematical tools for representing vagueness and uncertainty. We apply these models in combination to study vagueness and uncertainty in K-algebras. We introduce the notion of single-valued neutrosophic soft (SNS) K-algebras and investigate some of their properties. We establish the notion of ( ∈ , ∈ ∨ q ) -single-valued neutrosophic soft K-algebras and describe some of their related properties. We also illustrate the concepts with numerical examples. Full article
(This article belongs to the Special Issue Neutrosophic Topology)
8 pages, 240 KiB  
Article
Neutrosophic Triplet v-Generalized Metric Space
by Memet Şahin and Abdullah Kargın
Axioms 2018, 7(3), 67; https://doi.org/10.3390/axioms7030067 - 06 Sep 2018
Cited by 15 | Viewed by 3007
Abstract
The notion of Neutrosophic triplet (NT) is a new theory in Neutrosophy. Also, the v-generalized metric is a specific form of the classical metrics. In this study, we introduced the notion of neutrosophic triplet v-generalized metric space (NTVGM), and we obtained [...] Read more.
The notion of Neutrosophic triplet (NT) is a new theory in Neutrosophy. Also, the v-generalized metric is a specific form of the classical metrics. In this study, we introduced the notion of neutrosophic triplet v-generalized metric space (NTVGM), and we obtained properties of NTVGM. Also, we showed that NTVGM is different from the classical metric and neutrosophic triplet metric (NTM). Furthermore, we introduced completeness of NTVGM. Full article
(This article belongs to the Special Issue Neutrosophic Topology)
15 pages, 272 KiB  
Article
Relations between the Complex Neutrosophic Sets with Their Applications in Decision Making
by Ashraf Al-Quran and Shawkat Alkhazaleh
Axioms 2018, 7(3), 64; https://doi.org/10.3390/axioms7030064 - 01 Sep 2018
Cited by 16 | Viewed by 2967
Abstract
The basic aim of soft computing is to trade precision for a tractableness and reduction in solution cost by pushing the limits of tolerance for imprecision and uncertainty. This paper introduces a novel soft computing technique called complex neutrosophic relation (CNR) to evaluate [...] Read more.
The basic aim of soft computing is to trade precision for a tractableness and reduction in solution cost by pushing the limits of tolerance for imprecision and uncertainty. This paper introduces a novel soft computing technique called complex neutrosophic relation (CNR) to evaluate the degree of interaction between two complex neutrosophic sets (CNSs). CNSs are used to represent two-dimensional information that are imprecise, uncertain, incomplete and indeterminate. The Cartesian product of CNSs and subsequently the complex neutrosophic relation is formally defined. This relation is generalised from a conventional single valued neutrosophic relation (SVNR), based on CNSs, where the ranges of values of CNR are extended to the unit circle in complex plane for its membership functions instead of [0, 1] as in the conventional SVNR. A new algorithm is created using a comparison matrix of the SVNR after mapping the complex membership functions from complex space to the real space. This algorithm is then applied to scrutinise the impact of some teaching strategies on the student performance and the time frame(phase) of the interaction between these two variables. The notion of inverse, complement and composition of CNRs along with some related theorems and properties are introduced. The performance and utility of the composition concept in real-life situations is also demonstrated. Then, we define the concepts of projection and cylindric extension for CNRs along with illustrative examples. Some interesting properties are also obtained. Finally, a comparison between different existing relations and CNR to show the ascendancy of our proposed CNR is provided. Full article
(This article belongs to the Special Issue Neutrosophic Topology)
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