Loading article...
Loading article...
Stream/Area:
-
Subject:
-
Paper ID:
IJSREM66990
Volume:
10 |
8 |
Aug 2026
Pages:
1-12
Publication Frequency:
Monthly (12 issues per year)
License:International Journal of Scientific Research in Engineering and Management follows the Creative Commons Attribution 4.0 (CC BY 4.0) License, allowing free use and distribution with proper attribution.
MATHEMATICS
L.R.G. Government Arts College for Women,Tirupur -641604
MATHEMATICS
L.R.G. Government Arts College for Women,Tirupur -641604
This paper presents a systematic development of Neutrosophic Picture Fuzzy Topology (NPFT) as a generalized topological structure obtained by integrating neutrosophic logic with picture fuzzy set theory. Picture fuzzy sets extend intuitionistic fuzzy sets by admitting positive, neutral, and negative membership degrees, while neutrosophic logic independently characterizes truth, indeterminacy, and falsity, thereby enabling a richer representation of uncertainty. Within this framework, neutrosophic picture fuzzy sets and neutrosophic picture fuzzy topological spaces are formally introduced. Fundamental topological notions, including open and closed sets, interior, and closure operators, are defined and their essential properties are examined. Mappings between neutrosophic picture fuzzy topological spaces are also studied.In particular, Neutrosophic picture fuzzy continuous functions are defined and several of their properties are established, such as preservation under composition and their relationships with interior and closure operators. Representative examples are provided to illustrate the proposed concepts and validate the theoretical results. The resulting framework extends existing fuzzy and neutrosophic topological models and offers a coherent mathematical basis for addressing uncertainty and indeterminacy in non-classical settings.
KEYWORDS
In this paper, we introduced Neutrosophic Picture Fuzzy set,Neutrosophic Picture Fuzzy Topological spaces and investigated Neutrosophic Picture Fuzzy open and closed sets, Neutrosophic Picture Fuzzy interior,closure and Neutrosophic Picture Fuzzy continuous function.
1. Zadeh LA(1965) Fuzzy sets,Inf Control8(3):338-353. 2. Atanassov KT(1986) Intuitionistic fuzzy sets.Fuzzy Syst 20(1):87-96 3. B. C. Cuong, V. Kreinovich, Picture fuzzy sets-a new concept for computational intelligence problems in 2013 third world congress on information and communication technologies (WICT 2013), 1–6. 4. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182–190 5. Wang, H., Smarandanche, F., Zhang, Y. & Sunderraman, R. (2010). Single valued neutrosophic sets. Review of the Air Force Academy (Brasov), 1(16), 10-14. 6. Smarandache, F. (1998). Neutrosophy / Neutrosophic Probability, Set, and Logic. Proquest, Michigan, USA. 7. Cuong, B.C. (2014). Picture Fuzzy Sets. Journal of Computer Science and Cybernetics, 30(4), 409-420. 8. Karatas, Serkan and Cemil Kuru. "Neutrosophic Topology." Neutrosophic Sets and Systems 13, 1 (2016) 9. F. Smarandache, Neutrosophic set - a generalization of the intuitionistic fuzzy set, International Journal of Pure and Applied Mathematics, 24(3) (2005) 287–297. 10. A. Razaq, I. Masmali, H. Garg & U. Shuaib. Picture fuzzy topological spaces and associated continuous functions (AIMS Mathematics, June 2022).
Publication Date
8/28/2026
Peer Review Type
Double-Blind Peer Review
Review Rounds: 2
Documents
Article Views
0
Total views since publication
PDF Downloads
2
Total downloads since publication
Geographic Reach
5
Digital Preservation: This article is permanently archived on Zenodo and complies with all data preservation standards across major indexing platforms.
Plagiarism Screening
This manuscript has been checked for plagiarism using TurnitinPlagiarismChecker software.
Conflict of Interest
The authors declare no conflict of interest related to this research work.
Funding Information
No funding information available for this research.
Related research in the same subject area
Loading similar articles...