HyperFuzzy Control System and SuperHyperFuzzy Control System

• Takaaki Fujita

  Independent Researcher, Tokyo, Japan

  Author

• Arif Mehmood

  Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, KPK, Pakistan

  Author

• Arkan A. Ghaib

  Department of Information Technology, Management Technical College, Southern Technical University, Basrah, 61004, Iraq

  Author

Uncertainty modeling is fundamental to decision-making across diverse domains, and numerous frameworks—such as Fuzzy Sets, Rough Sets, Hyperrough Sets, Vague Sets, Intuitionistic Fuzzy Sets, Hesitant Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets—have been developed to capture different facets of imprecision.  Among these extensions are Hyperfuzzy Sets and their recursive generalization, SuperHyperfuzzy Sets, which assign set-valued membership degrees at multiple hierarchical levels.  This paper introduces the concepts of Hyperfuzzy Control Systems and (m,n)-SuperHyperfuzzy Control Systems, showing how they generalize classical fuzzy control by incorporating richer uncertainty structures.  We present rigorous definitions, theoretical properties, and illustrative examples demonstrating their ability to model hierarchical uncertainty in real-world control applications.

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