Fuzzy and Hyperfuzzy Perspectives on Length, Mean, and Dot in IUP-Algebras

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DOI: https://doi.org/10.28924/2291-8639-24-2026-255
Published: Aug 17, 2026
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Apichaya Arwut, Kanyanat Phuangma, Kittiyapron Thuanpung, Aiyared Iampan, Fuzzy and Hyperfuzzy Perspectives on Length, Mean, and Dot in IUP-Algebras, Int. J. Anal. Appl., 24 (2026), 255.

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Apichaya Arwut, Kanyanat Phuangma, Kittiyapron Thuanpung, Aiyared Iampan

Abstract

This paper studies fuzzy and hyperfuzzy perspectives on length, mean, and dot constructions in IUP-algebras. For a given hyperstructure over an IUP-algebra, three induced fuzzy structures are considered: the length obtained from the difference between the supremum and infimum values, the mean obtained from their average, and the dot obtained from their product. Based on these induced fuzzy structures, we introduce the notions of length fuzzy IUP-subalgebras, mean fuzzy IUP-subalgebras, and dot fuzzy IUP-subalgebras of types \(1\), \(2\), \(3\), and \(4\). Several basic properties and relationships among these types are investigated. In particular, we show that the type \(3\) case implies the type \(1\) case, the type \(2\) case implies the type \(4\) case, and the type \(2\) and type \(3\) cases coincide under the induced fuzzy structure. We also provide characterizations of length, mean, and dot fuzzy IUP-subalgebras in terms of upper level subsets, lower level subsets, and equal level subsets. Furthermore, we establish sufficient conditions connecting these induced fuzzy IUP-subalgebras with \((i,j)\)-hyperfuzzy IUP-subalgebras through the infimum and supremum fuzzy structures. Examples are given to illustrate the results and to show that some converse implications do not hold in general.

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