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Decision algorithm for educational institute selection with spherical fuzzy heronian mean operators and Aczel-Alsina
Abrar Hussain1, Kifayat Ullah1, Sajid Latif1
1Department of Mathematics, Riphah International University Lahore Campus, 54000, Lahore, Pakistan.
Heliyon
|April 11, 2024
Summary
This study introduces spherical fuzzy sets (SFSs) and Aczel Alsina operations for decision-making with complex data. New SFS Aczel Alsina Heronian mean operators enhance information aggregation and analysis for real-world problems.
Area of Science:
- Fuzzy Set Theory
- Decision Analysis
- Information Aggregation
Background:
- Spherical fuzzy sets (SFSs) offer a more comprehensive framework than intuitionistic and picture fuzzy sets.
- Decision-makers (DMs) face challenges with complicated and insufficient information during aggregation.
- Aczel Alsina triangular norms are recognized for their smooth approximation capabilities in decision analysis.
Purpose of the Study:
- To develop novel Aczel Alsina t-norm and t-conorm operations within the spherical fuzzy (SF) information context.
- To introduce new mathematical approaches for analyzing SF data, ensuring clarity and information sufficiency.
- To establish an algorithm for multiple attribute decision-making (MADM) problems using the proposed methods.
Main Methods:
- Development of spherical fuzzy Aczel Alsina Heronian mean (SFAAHrM) and weighted Heronian mean (SFAAWHrM) operators.
- Introduction of spherical fuzzy Aczel Alsina geometric Heronian mean (SFAAGHrM) and weighted geometric Heronian mean (SFAAWGHrM) operators.
- Characterization of properties to validate the effectiveness of the derived mathematical approaches.
Main Results:
- Novel SF Aczel Alsina Heronian mean operators and geometric variants were successfully developed.
- The proposed methods demonstrate validity and effectiveness through characterized properties.
- A numerical example confirmed the compatibility of the derived approaches for improving educational institute performance.
Conclusions:
- The study successfully integrated Aczel Alsina triangular norms with spherical fuzzy sets.
- The developed operators and MADM algorithm provide a robust mechanism for handling complex decision-making scenarios.
- The findings offer a solid foundation for enhancing the performance of organizations, particularly in educational settings.
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