Advanced Partitioned Neutrosophic Offsets, Oversets, and Undersets: Modeling “Neither Agree nor Disagree” and Beyond

Authors

  • Takaaki Fujita Independent Researcher, Tokyo, Japan
  • Raed Hatamleh Department of Mathematics, Faculty of Science, Jadara University, Irbid-Jordan
  • Ahmed Heilat Department of Mathematics, Faculty of Science, Jadara University, Irbid-Jordan https://orcid.org/0000-0002-9371-8286

DOI:

https://doi.org/10.19139/soic-2310-5070-3191

Keywords:

Neutrosophic Set, Hexapartitioned Neutrosophic Set, Octapartitioned Neutrosophic Set, Nonapartitioned Neutrosophic Set, Decapartitioned neutrosophic set, Neutrosophic Offset.

Abstract

Modern uncertainty-modeling frameworks-fuzzy sets, intuitionistic fuzzy sets, hyperfuzzy sets, neutrosophicsets, and plithogenic sets-provide powerful tools for capturing vagueness and imprecision. In particular, neutrosophic sets characterize each element by three independent degrees: truth, indeterminacy, and falsity. Classical neutrosophic sets have been refined by partitioning the membership degrees into additional components. Recently, the Hexapartitioned Neutrosophic Set, Octapartitioned Neutrosophic Set, Nonapartitioned Neutrosophic Set, and Decapartitioned Neutrosophic Set have been defined. In this paper, we introduce four novel partitioned models-hexapartitioned, octapartitioned, nonapartitioned, and decapartitioned neutrosophic offsets/oversets/undersets-and show how each can be seamlesslyembed ded into the plithogenic-set framework.

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Published

2026-01-29

How to Cite

Fujita , T., Hatamleh , R., & Heilat, A. (2026). Advanced Partitioned Neutrosophic Offsets, Oversets, and Undersets: Modeling “Neither Agree nor Disagree” and Beyond. Statistics, Optimization & Information Computing, 15(6), 5239–5283. https://doi.org/10.19139/soic-2310-5070-3191

Issue

Vol. 15 No. 6 (2026)

Section

Research Articles

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