On De-Roughication, De-Hyperization, and De-Nearization:Reduction Principles in Advanced Structural Systems

Authors

https://doi.org/10.48314/ijorai.v2i3.95

Abstract

This paper formalizes three “de-” processes that convert higher-order uncertainty into crisp structures. First, we define a costsensitive deroughication operator Dα,β that selects boundary elements by rough-membership thresh-olds; we prove sandwich, extremal, idempotence, and monotonicity properties and show it minimizes a risk. Second, we specify de-hyperization from (m, n)–SuperHyperStructures to HyperStructures and then to classical operations via lifting/flattening and a canonical selector, with a recovery result for lifted classical operations. Third, we introduce de-nearization DeNearε that removes conflicting descriptions to enforce an ε margin; we prove termination, separation, and maximality. Applications include medical triage, fraud screening, manufacturing, and transit.

Keywords:

De-roughication, De-hyperization, De-nearization, Rough set, HyperStructure, SuperHyperStructure, Near set

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Published

2026-09-08

Issue

Vol. 2 No. 3 (2026): International Journal of Operations Research and Artificial Intelligence (IJORAI)

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How to Cite

Fujita, T. . (2026). On De-Roughication, De-Hyperization, and De-Nearization:Reduction Principles in Advanced Structural Systems. International Journal of Operations Research and Artificial Intelligence , 2(3), 148-166. https://doi.org/10.48314/ijorai.v2i3.95

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