Hyperfuzzy and SuperHyperfuzzy Weighted Averages

  • Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan
  • Iqbal M. Batiha Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
  • Nidal Anakira Faculty of Education and Arts, Sohar University, Sohar 311, Oman
  • Mohammad S. Hijazi Department of Mathematics, College of Sciences, Jouf University, Sakaka, Saudi Arabia
  • Areen Al-Khateeb Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan
  • Tala Sasa Department of Mathematics, Applied Science Private University, Amman 11937, Jordan
DOI: https://doi.org/10.19139/soic-2310-5070-3092
Keywords: Fuzzy set, HyperFuzzy Set, SuperHyperFuzzy Set, HyperFuzzy Weighted Average, SuperHyper- Fuzzy Weighted Average

Abstract

Uncertainty modeling is fundamental to decision‑making across diverse domains, and numerous frameworks, such as Fuzzy Sets, Rough Sets, Hesitant Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets, have been developed to capture different facets of imprecision. Among these, Hyperfuzzy Sets and their recursive generalization, SuperHyperfuzzy Sets, assign set‑valued membership degrees at multiple hierarchical levels to represent uncertainty more richly. A Fuzzy Weighted Average computes a weighted mean of fuzzy numbers by applying the extension principle to their membership functions. In this paper, we extend this concept by defining the Hyperfuzzy Weighted Average and the SuperHyperfuzzy Weighted Average based on Hyperfuzzy and SuperHyperfuzzy Sets. We present formal definitions, prove key properties, such as well‑definedness, reduction to classical cases, and idempotency, and illustrate their application through examples, demonstrating enhanced aggregation of multi‑level uncertainty.
Published
2026-02-25
How to Cite
Fujita, T., Batiha, I. M., Anakira, N., Hijazi, M. S., Al-Khateeb, A., & Sasa, T. (2026). Hyperfuzzy and SuperHyperfuzzy Weighted Averages. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3092
Issue
Online First
Section
Research Articles
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