A robust E learning recommendation system based on novel interval valued bipolar fuzzy hypersoft set theory

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 (UVBF_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 (IVBFHSS) 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.