A New Framework of Neutrosophic Picture Fuzzy Sets and Topological Space

M. Sathiya; P. Senthil Vaidu; P. Jayakumar

doi:https://doi.org/10.14445/22315373/IJMTT-V72I8P104

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 8 | Year 2026 | Article Id. IJMTT-V72I8P104 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I8P104

A New Framework of Neutrosophic Picture Fuzzy Sets and Topological Space

M. Sathiya, P. Senthil Vaidu, P. Jayakumar

Received	Revised	Accepted	Published
22 Jun 2026	25 Jul 2026	15 Aug 2026	29 Aug 2026

Citation :

M. Sathiya, P. Senthil Vaidu, P. Jayakumar, "A New Framework of Neutrosophic Picture Fuzzy Sets and Topological Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 8, pp. 27-38, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I8P104

Abstract

In this paper, the concept of the Neutrosophic Picture Fuzzy Sets (NPFS) is introduced by combining the ideas of the neutrosophic sets, fuzzy sets, and picture fuzzy sets, which can be applied in more complex uncertain situations than the fuzzy set and picture fuzzy set. The mathematical model of NPFS and their topological structure, namely, Neutrosophic Picture Fuzzy Topological Spaces (NPFTS), are presented. The study highlights the main properties of NPFS and NPFTS and provides the basic operations with NPFSs. The operations have been applied for solving decision-making problems with incomplete, consistent and conflicting information as well as for other purposes connected with NPFSs and NPFTSs. The paper includes illustrative examples of NPFS, NPFTS and their operations.

Keywords

Neutrosophic Picture Fuzzy Sets, Neutrosophic Picture Fuzzy Topological Spaces, Neutrosophic Picture Fuzzy Pre, Semi, Regular, b,𝛼 and 𝛽 Open Sets.

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