Abstract
Understanding bipolar information is crucial as it enables individuals to make informed decisions that consider both extremes of a spectrum, leading to more balanced and effective outcomes. Interval-valued bipolar fuzzy set (IVBFS) has already been introduced in the literature as a great decision-making tool that can capture interval-valued bipolar information to properly address uncertainty. In this article, we introduce a hybrid of Interval-valued bipolar fuzzy set (IVBFS) and bipolar hypersoft sets (BHSS) called interval-valued bipolar fuzzy hypersoft set \((IVBF_{HSS})\), which merges the capabilities of IVBFS and BHSS. The rationale behind the design of the presented data structure is to manipulate and process information in decision-making scenarios when the data is bipolar, has multiple attributes that need to be addressed up to a sub-attributive level to get a proper representation of the data provided, and needs to be presented in the form of intervals. In \((IVBF_{HSS})\), two hyper soft sets (HSSs) are used, one providing positive interval-valued membership information and the other providing negative interval-valued membership information. We outline the essential features and basic operations of \((IVBF_{HSS})\) in this paper, examining its commutative, associative, distributive, and De Morgan laws to ensure a comprehensive analysis. To demonstrate the significance of \((IVBF_{HSS})\), we develop a preferential decision support algorithm for selecting the best alternative in e-learning, such as identifying the most suitable instructional method, which can effectively be formulated as a Multi-Attribute Decision-Making (MADM) problem. This approach allows for the systematic evaluation of various alternatives based on multiple parameters and sub-parameters, enabling a rational and well-informed decision. This algorithm helps select the best alternative from a given set of options, leveraging the versatile nature of \((IVBF_{HSS})\). The presented study conducts both computation-based and structural comparisons to evaluate the adaptability and reliability of the proposed framework.
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All data generated or analysed during this study is included in the article.
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All code used to produce the computational results is provided in the Supplementary Information in the file titled “IVBFHSS.xlxs”.
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Muhammad Imran Harl: Writing – original draft, Methodology, Formal analysis, Investigation: Muhammad Saeed: Conceptualization, Supervision, Validation, Writing – review & editing: Muhammad Haris Saeed: Writing – original draft, Software, Writing – review & editing: Muhammad Salman Habib: Investigation, Funding Acquisition, Validation, Writing – review & editing, Resources: Seung-June Hwang: Resources, Writing – review & editing, Funding Acquisition, Validation
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Harl, M.I., Saeed, M., Saeed, M.H. et al. A robust E learning recommendation system based on novel interval valued bipolar fuzzy hypersoft set theory. Sci Rep (2026). https://doi.org/10.1038/s41598-026-42231-6
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DOI: https://doi.org/10.1038/s41598-026-42231-6
