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Complex Diophantine interval-valued Pythagorean normal set for decision-making processes.
Murugan Palanikumar1, Nasreen Kausar2, Ponnaiah Tharaniya3
1Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, India.
Scientific Reports
|January 4, 2025
Summary
A novel method using complex Diophantine interval-valued Pythagorean normal sets (CDIVPNS) enhances multi-attribute decision-making. This approach improves robotic system evaluation by considering tasks, precision, speed, and work completion.
Area of Science:
- Decision Sciences
- Computational Mathematics
- Artificial Intelligence
Background:
- Multiple-attribute decision-making (MADM) challenges require robust mathematical frameworks.
- Existing methods may not adequately handle complex, interval-valued, and Pythagorean data.
- Robotic system evaluation necessitates precise and efficient decision-making models.
Purpose of the Study:
- To introduce a novel method for MADM using complex Diophantine interval-valued Pythagorean normal sets (CDIVPNS).
- To explore and define various aggregation operations (weighted averaging, weighted geometric) within the CDIVPNS framework.
- To demonstrate the algebraic properties and practical applicability of the proposed CDIVPNS model.
Main Methods:
- Development of aggregation operators: CDIVPN weighted averaging (CDIVPNWA), CDIVPN weighted geometric (CDIVPNWG), generalized CDIVPN weighted averaging (CGDIVPNWA), and generalized CDIVPN weighted geometric (CGDIVPNWG).
- Calculation of weighted average and geometric distance using an established aggregating model.
- Analysis of algebraic structures (associative, distributive, idempotent, bounded, commutative, monotonic) satisfied by CDIVPNS.
- Evaluation of score and accuracy values with real-world examples.
Main Results:
- CDIVPNS demonstrate desirable algebraic properties, ensuring model stability and reliability.
- The proposed aggregation operators effectively handle complex decision-making scenarios.
- A numerical example and flowchart illustrate the practical application of the CDIVPNS model.
- Comparative analysis confirms the superiority of the proposed approach over existing methods.
Conclusions:
- The CDIVPNS framework offers a powerful and flexible tool for complex MADM problems.
- The developed aggregation operators provide enhanced capabilities for decision analysis.
- The method shows significant potential for improving the evaluation and performance of robotic systems.
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