T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making

Area of Science:

• Fuzzy Set Theory
• Decision Sciences
• Information Fusion

Background:

• T-spherical fuzzy sets (T-SFSs) offer a robust framework for uncertainty by incorporating four membership degrees: membership, abstinence, non-membership, and refusal.
• Existing fuzzy set theories have limitations in comprehensively handling complex uncertain information.
• Power operators effectively capture relationships between attributes, crucial for aggregation.

Purpose of the Study:

• To introduce and define novel power aggregation operators tailored for T-spherical fuzzy sets (T-SFSs).
• To develop weighted averaging and geometric power aggregation operators for T-SFSs.
• To establish a multiple attribute decision-making (MADM) algorithm utilizing these new operators.

Main Methods:

• Definition of T-spherical fuzzy weighted, ordered weighted, hybrid averaging, and geometric power aggregation operators.
• Derivation of properties and analysis of special cases for the proposed operators.
• Development and application of a MADM algorithm based on the new operators.

Main Results:

• Introduction of several new power aggregation operators for T-SFSs, including weighted averaging and geometric types.
• Analysis of the properties and constraints of the proposed operators.
• Demonstration of the operators' efficacy through a MADM algorithm applied to uncertain information problems.

Conclusions:

• The proposed power aggregation operators for T-SFSs provide a powerful tool for managing and aggregating uncertain information.
• The developed MADM algorithm effectively utilizes these operators to solve complex decision-making problems.
• Comparative analysis confirms the superiority and effectiveness of the proposed approach.