Some Einstein interaction geometric aggregation operators based on improved operational laws of complex q-rung orthopair fuzzy set and their applications

Complex q-rung orthopair fuzzy (CQROF) set is very feasible to depict the complex uncertain information in real-life problems because it is the modified concept from the complex Pythagorean and complex intuitionistic fuzzy sets. In this manuscript, we concentrate to analyze the improved Einstein operational laws for CQROF information. Then, based on the improved Einstein operational laws, we develop the complex q-rung orthopair fuzzy Einstein interaction weighted geometric (CQROFEIWG) operator, complex q-rung orthopair fuzzy Einstein interaction ordered weighted geometric (CQROFEIOWG) operator, and complex q-rung orthopair fuzzy Einstein interaction hybrid geometric (CQROFEIHG) operator. Furthermore, we analyze their major results and main three properties such as idempotency, boundedness, and monotonicity. Additionally, a decision-making approach with complex q-rung orthopair fuzzy information is developed, in which weights are handled objectively. Finally, some illustrated examples are used to demonstrate the supremacy and feasibility of the proposed approaches by comparing them with some existing ones.

Automated summary

The complex q-rung orthopair fuzzy (CQROF) set is proposed to represent complex uncertain information, and the improved Einstein operational laws are analyzed in this manuscript. Based on the improved laws, the complex q-rung orthopair fuzzy Einstein interaction weighted geometric (CQROFEIWG) operator, complex q-rung orthopair fuzzy Einstein interaction ordered weighted geometric (CQROFEIOWG) operator, and complex q-rung orthopair fuzzy Einstein interaction hybrid geometric (CQROFEIHG) operator are developed. The major results and properties such as idempotency, boundedness, and monotonicity are analyzed. Furthermore, a decision-making approach with complex q-rung orthopair fuzzy information is developed, demonstrating its superiority and feasibility through illustrated examples compared with existing approaches.