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Group decision-making algorithm with sine trigonometric r,s,t-spherical fuzzy aggregation operators and their

Muhammad Azeem¹, Ayesha Ilyas¹, Jawad Ali²

¹Department of Mathematics and Statistics, University of Agriculture, Faisalabad, 38000, Pakistan.

Scientific Reports

|May 11, 2024

Summary

This study introduces sine trigonometric laws to enhance r, s, t-spherical fuzzy (r, s, t-SPF) sets for decision-making. New aggregation operators and a group decision-making algorithm are developed and validated with a laptop selection example.

Keywords:

Aggregation operators MAGDM Trigonometric operations r-s-t-spherical fuzzy set

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Area of Science:

Decision Sciences
Fuzzy Set Theory
Computational Intelligence

Background:

Traditional fuzzy sets have limitations in handling complex uncertainties.
Spherical fuzzy sets offer enhanced flexibility with parameters r, s, and t.
There is a need for advanced mathematical frameworks to improve decision-making under uncertainty.

Purpose of the Study:

To introduce sine trigonometric laws for enhancing r, s, t-spherical fuzzy (r, s, t-SPF) sets.
To design novel aggregation operators (AOs) based on these sine trigonometric laws.
To develop a multiple attribute group decision-making (MAGDM) algorithm using the proposed AOs.

Main Methods:

Integration of sine trigonometric functions into the r, s, t-SPF framework.
Development of new aggregation operators tailored for r, s, t-SPF data.
Construction of a MAGDM algorithm incorporating the novel AOs.
Application to a practical laptop selection problem for validation.

Main Results:

Sine trigonometric laws successfully enhance the applicability of r, s, t-SPF sets.
Newly designed AOs exhibit desirable mathematical properties under sine trigonometric functions.
The proposed MAGDM algorithm effectively addresses complex decision-making scenarios.
Parameter analysis and comparative studies confirm the superiority of the developed AOs.

Conclusions:

The sine trigonometric approach provides a robust enhancement for r, s, t-SPF sets.
The developed AOs and MAGDM algorithm offer a powerful tool for uncertainty management in decision-making.
This research advances the theoretical foundation and practical application of fuzzy set theory in complex decision problems.