Aggregation operators based on Einstein averaging under q-spherical fuzzy rough sets and their applications in...

Area of Science:

• Mathematics
• Computer Science
• Decision Science

Background:

• Handling complex and uncertain data is a significant challenge in decision-making.
• Existing aggregation operators may lack the precision required for nuanced data types.
• Q-spherical fuzzy rough sets offer a framework for representing complex uncertainty.

Purpose of the Study:

• To introduce innovative operational laws and aggregation algorithms for q-spherical fuzzy rough data.
• To develop and present three novel Einstein averaging operators: weighted, ordered weighted, and hybrid weighted averaging.
• To demonstrate the applicability and efficacy of these operators in attribute decision-making scenarios.

Main Methods:

• Development of new operational laws based on Einstein operations for q-spherical fuzzy rough sets.
• Design of three novel aggregation operators: q-spherical fuzzy rough Einstein weighted averaging, ordered weighted averaging, and hybrid weighted averaging.
• Implementation and validation of the proposed operators in attribute decision-making problems with q-spherical fuzzy rough data.

Main Results:

• The proposed Einstein averaging operators enhance precision and accuracy in arithmetic averaging for q-spherical fuzzy rough data.
• The study demonstrates the practical implementation and effectiveness of these operators in attribute decision-making.
• Comparative and sensitivity analyses confirm the robustness and advantages of the proposed methods over existing approaches.

Conclusions:

• The newly developed operators and algorithms provide effective tools for decision-making with complex and uncertain q-spherical fuzzy rough data.
• The research contributes novel methods that enrich the understanding and application of fuzzy rough set theory.
• The findings highlight the potential for significant practical applications in various decision-making processes involving ambiguity.