Multi-Attribute Decision Making with Einstein Aggregation Operators in Complex Q-Rung Orthopair Fuzzy Hypersoft...

Area of Science:

• Fuzzy Set Theory
• Decision Making
• Information Granularity

Background:

• Human interpretations often involve imprecision and ambiguity.
• Existing fuzzy set theories, such as complex intuitionistic and Pythagorean fuzzy sets, have limitations in capturing complex, multi-dimensional data.
• There is a need for more generalized mathematical tools to handle such data effectively.

Purpose of the Study:

• To introduce and formalize the concept of the complex q-rung orthopair fuzzy hypersoft set (Cq-ROFHSS).
• To extend the capabilities of fuzzy set theory for modeling complex, imprecise, and contradictory two-dimensional data.
• To develop multi-attribute decision-making algorithms based on the proposed Cq-ROFHSS framework.

Main Methods:

• Development of the Cq-ROFHSS by combining the parametric structures of complex q-rung orthopair fuzzy sets and hypersoft sets.
• Establishment of basic set-theoretic operations and properties for Cq-ROFHSS.
• Introduction of Einstein operations and aggregation operators for Cq-ROFHSS values.
• Development of two multi-attribute decision-making algorithms using score and accuracy functions.

Main Results:

• The proposed Cq-ROFHSS framework effectively captures a greater degree of imprecision and ambiguity compared to existing theories.
• The developed decision-making algorithms successfully prioritize ideal schemes in periodically inconsistent datasets.
• A case study on distributed control systems demonstrates the feasibility and rationality of the Cq-ROFHSS approach.
• Comparative analysis confirms the flexibility, validity, and superiority of the proposed model over mainstream technologies.

Conclusions:

• The Cq-ROFHSS is a powerful and flexible extension of fuzzy set theory for handling complex, multi-parameterized, and imprecise data.
• The developed decision-making algorithms provide an effective method for analyzing and prioritizing complex decision problems.
• The research contributes a valuable mathematical tool for applications requiring the modeling of nuanced and contradictory information.