On the Structure and Properties of Hyperfuzzy and SuperhyperfuzzyIntervals

Authors

https://doi.org/10.22105/scfa.vi.70

Abstract

A fuzzy set assigns to each element in a universe a membership degree in the interval [0, 1], effectively modeling imprecision and vagueness. A hyperfuzzy set extends this concept by mapping each element to a
nonempty subset of [0, 1], thereby representing multiple possible membership degrees and capturing both uncertainty and variability. An m, n-superhyperfuzzy set further generalizes this structure by assigning to
each nonempty element of the mth and the nth power-set hierarchy a nonempty subset of [0, 1], enabling the modeling of hierarchical and nested uncertainty. A fuzzy interval is a special kind of fuzzy set on R
that is both normal and convex, with each α-cut forming a nonempty closed interval, thus providing a precise framework for modeling uncertain numerical values. In this paper, we introduce and define the notions of Hyperfuzzy Interval and SuperHyperfuzzy Interval, and provide a brief investigation of their mathematical properties.

Keywords:

Set theory, Hyperfuzzy interval, Fuzzy interval, Hyperfuzzy set, Superhyperfuzzy set

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Published

2026-03-16

Issue

Vol. 3 No. 1 (2026): Soft Computing Fusion with Applications

Section

Articles

How to Cite

Fujita, T. . (2026). On the Structure and Properties of Hyperfuzzy and SuperhyperfuzzyIntervals. Soft Computing Fusion With Applications , 3(1), 10-26. https://doi.org/10.22105/scfa.vi.70

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