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https://doi.org/10.31224/4967...
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Linear Diophantine HyperFuzzy Set and SuperHyperFuzzy Set

Authors: Takaaki Fujita;

Linear Diophantine HyperFuzzy Set and SuperHyperFuzzy Set

Abstract

Uncertainty modeling underpins decision-making across diverse domains, and numerous frameworks—such as Fuzzy Sets [1, 2], Rough Sets [3, 4], Hesitant Fuzzy Sets [5, 6], and Plithogenic Sets [7, 8]—have been developed to capture different facets of imprecision. Hyperfuzzy Sets and their recursive generalization, SuperHyperfuzzy Sets, assign set-valued membership degrees at multiple hierarchical levels to represent uncertainty more richly [9]. The Linear Diophantine Fuzzy Set further refines this approach by imposing weighted linear Diophantine constraints on membership and non-membership grades [10–13]. In this paper, we define two new constructs—the Linear Diophantine Hyperfuzzy Set and the Linear Diophantine SuperHyperfuzzy Set—by integrating Diophantine constraints with hyperfuzzy and superhyperfuzzy frameworks, and we present a concise application example. These extensions offer a more structured, hierarchical means of applying Linear Diophantine Fuzzy Set methodology in practical uncertain environments.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
hybrid