Exploring Neutrosophic Set Variants: Investigating Topological Insights, Approximation Spaces and Decision-Making Approaches
| dc.contributor.author | Bhuvaneshwari S | |
| dc.contributor.author | Guide - Dr. C.Antony Crispin Sweety | |
| dc.date.accessioned | 2026-02-17T08:51:42Z | |
| dc.date.available | 2026-02-17T08:51:42Z | |
| dc.date.issued | 2025-08 | |
| dc.description.abstract | List of Notations and Abbreviations : FS Fuzzy Set IVFS Interval Valued Fuzzy Set IFS Intuitionistic Fuzzy Set NS Neutrosophic Set SVNS Single Valued Neutrosophic Set TFS Temporal Fuzzy Set TIFS Temporal Intuitionistic Fuzzy Set PFS Pythagorean Fuzzy Set SFS Spherical Fuzzy Set PNS Pythagorean Neutrosophic Set NSS Neutrosophic Spherical Set FNS Fermatean Neutrosophic Set FTNS Fermatean Temporal Neutrosophic Set IVFNS Interval Valued Fermatean Neutrosophic Set FNCS Fermatean Neutrosophic Cubic Set PNT Pythagorean Neutrosophic Topology PNP Pythagorean Neutrosophic Point PNTS Pythagorean Neutrosophic Topological Space PNN Pythagorean Neutrosophic Neighbourhood PNOS Pythagorean Neutrosophic Open Set PNCS Pythagorean Neutrosophic Closed Set NST Neutrosophic Spherical Topology NSTS Neutrosophic Spherical Topological Space NSP Neutrosophic Spherical Point NSN Neutrosophic Spherical Neighbourhood NSOS Neutrosophic Spherical Open Set NSCS Neutrosophic Spherical Closed Set FNT Fermatean Neutrosophic Topology FNTS Fermatean Neutrosophic Topological Space FNP Fermatean Neutrosophic Point FNN Fermatean Neutrosophic Neighbourhood FNOS Fermatean Neutrosophic Open Set FNCS Fermatean Neutrosophic Closed Set BT-FNS Bitopologies of Fermatean Neutrosophic Set BT-FNSubs Bitopologies of Fermatean Neutrosophic Subsets FTNS Fermatean Temporal Neutrosophic Set FNGO Fermatean Neutrosophic Gradation of Openness FNGC Fermatean Neutrosophic Gradation of Closedness gp- map Gradation preserving map In-BTF Category of all-inclusive BT-FNSubs and continuous functions FNr-top Category of rth graded FNTSs and gp-maps FT-NTS Fermatean Temporal Neutrosophic Topological Spaces SFT-NT Fermatean Temporal Neutrosophic Topology in Šostak’s sense CFT-NT Fermatean temporal neutrosophic topology in Chang’s sense LFT-NT Fermatean Temporal neutrosophic topology in Lowen’s sense FTN- closed Fermatean Temporal Neutrosophic closed FTNRS Fermatean Temporal Neutrosophic Rough Set FNRAS Fermatean Neutrosophic Rough Approximation Space FN-r Fermatean Neutrosophic relation LT Linguistic Term MCDM Multi-Criteria Decision-Making CODAS Combinative Distance-Based Assessment ÐϺ Decision Maker SWAM Spherical Weighted Arithmetic Mean SWGM Spherical Weighted Geometric Mean FWAM Fermatean Weighted Arithmetic Mean FWGM Fermatean Weighted Geometric Mean D-Mx Decision Matrix NS D-Mx Neutrosophic Spherical Decision Matrix FN D-Mx Fermatean Neutrosophic Decision Matrix PIS Positive Ideal Solution NIS Negative Ideal Solution SF Score Function AC Accuracy Function TMNSDM Tangent Metric Neutrosophic Spherical Distance Measure TMFNDM Tangent Metric Fermatean Neutrosophic Distance Measure TOPSIS Technique for Order Preference by Similarity to Ideal Solution ED Euclidean distance N-ED Normalized Euclidean Distance HD Hamming Distance N-HD Normalized Hamming Distance SMSVND Sine Metric Single- Valued Neutrosophic Distance : The scope of this thesis is to explore some of the existing neutrosophic variants and introduce some new types of neutrosophic variants. The notion of extended Pythagorean neutrosophic set, neutrosophic spherical set, and Fermatean neutrosophic set has been examined and the concepts of topology, rough set, operators, and measures has been developed and analysed. The idea of the proposed logic is extended to define Fermatean neutrosophic cubic set to manage high levels of uncertainty and vagueness and also to introduce Fermatean temporal neutrosophic set to deal with time moments. Further, the thesis combines rough set concept with Fermatean temporal neutrosophic set to construct a new class of rough set called Fermatean temporal neutrosophic rough set. A new class of aggregation operators for neutrosophic variant has been developed and used in a COmbinative Distance-based ASsessment (CODAS) evaluation method. Furthermore, tangent metric neutrosophic spherical distance measure and tangent metric Fermatean neutrosophic distance measure are formulated and applied to the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. Illustrative examples have been provided to validate and compare the defined aggregation operators and distance measures. | |
| dc.identifier.uri | https://ir.avinuty.ac.in/handle/123456789/18202 | |
| dc.language.iso | en | |
| dc.publisher | Avinashilingam | |
| dc.subject | Mathematics | En |
| dc.title | Exploring Neutrosophic Set Variants: Investigating Topological Insights, Approximation Spaces and Decision-Making Approaches | |
| dc.type | Learning Object |
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