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Classification of possible solutions regarding business engineering problems by using complex Pythagorean fuzzy rough
Tahir Mahmood1, Walid Emam2, Jabbar Ahmmad3
1Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan. tahirbakhat@iiu.edu.pk.
Scientific Reports
|May 13, 2025
Summary
This study introduces a complex Pythagorean fuzzy rough set to address business engineering challenges like complexity and resource constraints. The new framework aids in classifying solutions for complex business problems.
Area of Science:
- Business Engineering
- Information Science
- Decision Science
Background:
- Business engineering faces challenges including complexity, rapid technological change, resource limitations, and interdisciplinary collaboration.
- Existing methods may struggle with advanced data and risk data loss when addressing these complex issues.
- A need exists to classify solutions for these multifaceted business engineering problems.
Purpose of the Study:
- To develop a novel mathematical framework for addressing complex business engineering challenges.
- To introduce a complex Pythagorean fuzzy rough set, extending Tamir's complex fuzzy set concept.
- To establish aggregation operators and decision-making techniques for practical application.
Main Methods:
- Development of a complex Pythagorean fuzzy rough set based on Tamir's complex fuzzy set.
- Formulation of basic operational laws using Yager's t-norm and t-conorm.
- Initiation of complex Pythagorean fuzzy rough Yager weighted average and geometric aggregation operators.
- Introduction of the WASPAS (Weighted Aggregated Sum Product Assessment) technique for MADM problems.
Main Results:
- The proposed complex Pythagorean fuzzy rough set provides a robust method for handling uncertainty and complexity.
- New aggregation operators (Yager weighted average and geometric) are defined for the new set structure.
- The WASPAS technique, utilizing the new framework, is demonstrated for classifying business engineering solutions.
- An illustrative example and comparative analysis validate the effectiveness and advantages of the introduced theory.
Conclusions:
- The developed complex Pythagorean fuzzy rough set offers a powerful tool for managing complexity and uncertainty in business engineering.
- The new aggregation operators and WASPAS technique provide enhanced capabilities for decision-making in complex business environments.
- This research contributes a novel approach to classifying solutions for critical business engineering challenges, improving data handling and reducing data loss.
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