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A robust E learning recommendation system based on novel interval valued bipolar fuzzy hypersoft set theory
Muhammad Imran Harl1, Muhammad Saeed1, Muhammad Haris Saeed2
1Department of Mathematics, University of Management and Technology, Lahore, 54700, Punjab, Pakistan.
Scientific Reports
|March 13, 2026
Summary
This study introduces a novel interval-valued bipolar fuzzy hypersoft set (IVBFHS) for decision-making with bipolar information. The new framework enhances multi-attribute decision-making (MADM) by processing complex, interval-based data effectively.
Area of Science:
- Fuzzy Set Theory
- Decision Support Systems
- Multi-Attribute Decision-Making (MADM)
Background:
- Bipolar information is crucial for balanced decision-making, requiring tools that handle uncertainty.
- Interval-valued bipolar fuzzy sets (IVBFS) offer a way to capture interval-valued bipolar information.
- Bipolar hypersoft sets (BHSS) provide a framework for multi-attribute analysis up to sub-attributive levels.
Purpose of the Study:
- To introduce a hybrid data structure, the interval-valued bipolar fuzzy hypersoft set (IVBFHS).
- To merge the capabilities of IVBFS and BHSS for processing bipolar, interval-based, multi-attribute data.
- To develop a decision support algorithm for MADM problems using the proposed IVBFHS framework.
Main Methods:
- Development of the interval-valued bipolar fuzzy hypersoft set (IVBFHS) data structure.
- Analysis of fundamental operations and properties (commutative, associative, distributive, De Morgan laws) of IVBFHS.
- Creation of a preferential decision support algorithm for selecting optimal alternatives in e-learning scenarios.
Main Results:
- The proposed IVBFHS effectively manipulates and processes bipolar information presented in intervals across multiple attributes and sub-attributes.
- Essential features and operations of IVBFHS are defined and analyzed, ensuring its mathematical soundness.
- A decision support algorithm based on IVBFHS demonstrates adaptability and reliability in MADM problems, validated through computation and structural comparisons.
Conclusions:
- The interval-valued bipolar fuzzy hypersoft set (IVBFHS) is a powerful extension for handling complex decision-making scenarios with bipolar, interval-valued, and multi-attribute data.
- The developed decision support algorithm provides a systematic approach for rational decision-making, particularly applicable in fields like e-learning.
- The study validates the proposed framework's effectiveness and reliability for advanced decision support applications.
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