Iterative Refinement in Neutrosophic Logic: A Unified Framework for n-Refined and Partitioned Neutrosophic Models

Authors

  • Takaaki Fujita Independent Researcher, Tokyo, Japan Author

DOI:

https://doi.org/10.64060/ANMIV1i33

Keywords:

Iterative Refined Neutrosophic Logic, Refined quadripartitioned Neutrosophic Logic, Refined pentapartitioned Neutrosophic Logic, Refined heptapartitioned Neutrosophic Logic

Abstract

A Neutrosophic Set models uncertainty via three memberships—truth, indeterminacy, and falsity. We develop an n–Refined Neutrosophic Logic (n–RNL) that splits these into interpretable subcomponents and define refined quadripartitioned, pentapartitioned, and heptapartitioned families capturing contradiction, ignorance, unknown, and relative truth/falsity. Connectives are given blockwise by a t–norm/t–conorm pair. We prove merge/split homomorphisms that (i) reduce refined models to classical ones and (ii) embed unrefined semantics into refined spaces. We further introduce Iterative Refined Neutrosophic Logic (IRNL), allowing repeated, symmetric refinements with functorial stability of evaluations. Numerical examples from clinical decision support, autonomous driving, and fraud detection illustrate granular reasoning under heterogeneous evidence and priority schemes.

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Published

2026-10-20

Issue

Vol. 1 No. 3 (2026)

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Copyright (c) 2026 Takaaki Fujita (Author)

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Iterative Refinement in Neutrosophic Logic: A Unified Framework for n-Refined and Partitioned Neutrosophic Models. (2026). Advances in Neutrosophic Mathematics and Informatics, 1(3). https://doi.org/10.64060/ANMIV1i33
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