A novel algorithmic multi-attribute decision-making framework for solar panel selection using modified aggregations...

Area of Science:

• Fuzzy Set Theory
• Decision Science
• Multi-criteria Decision Making

Background:

• Cubic intuitionistic fuzzy sets (CIFSs) have limitations for multi-argument approximate functions.
• Existing models lack sufficient flexibility for complex parameter evaluations.

Purpose of the Study:

• To introduce and define the cubic intuitionistic fuzzy hypersoft set (Ω-set) as an extension of CIFSs.
• To develop novel operations and explore theoretical properties of Ω-sets.
• To present a practical algorithm for decision-making problems using Ω-sets.

Main Methods:

• Definition of Ω-set, associating sub-parametric tuples with CIFSs.
• Introduction of complement, P-order, R-order subsets, P-union, R-union, P-intersection, and R-intersection operations for Ω-sets.
• Development of internal ( $$ -set) and external ( $$ -set) cubic intuitionistic fuzzy hypersoft sets.
• Formulation of theorems and a decision-making algorithm based on Ω-set operations.

Main Results:

• The proposed Ω-set framework effectively addresses limitations of CIFSs for multi-argument functions.
• New operations and internal/external set concepts are defined and illustrated with examples.
• The study presents theoretical underpinnings for Ω-sets, including significant theorems.
• A practical algorithm is developed for solar panel selection in solar plant establishment.

Conclusions:

• The cubic intuitionistic fuzzy hypersoft set (Ω-set) offers a robust framework for complex decision-making.
• The developed operations and theoretical results provide a foundation for further research in fuzzy set theory.
• The proposed algorithm demonstrates the practical applicability of Ω-sets in real-world optimization scenarios like renewable energy selection.