The Hyperfuzzy AHP and Hyperfuzzy TOPSIS Methods for Multi-Criteria Decision-Making under Hierarchical Uncertainty

Takaaki Fujita; Talal Al-Hawary; Ajoy Kanti Das; Arif Mehmood

doi:10.65069/smart00202710

Authors

Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Author https://orcid.org/0009-0007-1509-2728
Talal Al-Hawary Department of Mathematics, Yarmouk University, Irbid, Jordan. Author https://orcid.org/0000-0002-5167-5265
Ajoy Kanti Das Department of Mathematics, Tripura University, Tripura, India. Author https://orcid.org/0000-0002-9326-1677
Arif Mehmood Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, Pakistan Author https://orcid.org/0000-0002-6230-9236

DOI:

https://doi.org/10.65069/smart00202710

Keywords:

AHP, HyperFuzzy Set, TOPSIS, SuperHyperFuzzy Set

Abstract

Fuzzy sets, rough sets, intuitionistic fuzzy sets, neutrosophic sets hyperneutrosophic sets, plithogenic sets, and other frameworks for handling uncertainty are actively being studied. Among the various extensions of fuzzy sets, Hyperfuzzy Sets and Super-Hyper-fuzzy Sets are particularly significant. These concepts are known for their ability to effectively address hierarchical uncertainty. Moreover, decision-making and fuzzy sets are frequently explored together, with wellknown frameworks such as AHP, TOPSIS, and MCDM forming the foundation of many studies.
In this paper, we propose new definitions of Hyperfuzzy AHP, Hyperfuzzy TOPSIS, Super-Hyper-fuzzy AHP, and Super-Hyper-fuzzy TOPSIS. These are natural extensions of fuzzy AHP and fuzzy TOPSIS that incorporate the structure of Hyperfuzzy Sets and Super-Hyper-fuzzy Sets. Our goal is to contribute to the modeling and analysis of real-world decision problems characterized by complex and hierarchical uncertainty, thereby enabling more flexible and robust decision-making frameworks.

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