A Multi-attribute Decision-Making Method with Complex q-Rung Orthopair Fuzzy Soft Information Based on Einstein Geometric Aggregation Operators

Complex a-rung orthopair fuzzy soft (CQROFS) set is very famous and effective tool for depicting complex uncertain information because it is the combination of the complex q-rung orthopair fuzzy set (CQROFS) and soft set (SS), in which the truth grade and falsity grade are expressed by complex numbers. Furthermore, Einstein's t-norm and t-conorm are very useful and more dominant tools in aggregating the collection of information into a singleton one, where the algebraic t-norm and t-conorm are the specific case of the Einstein t-norm and t-conorm. In this paper, we aim to propose the complex q-rung orthopair fuzzy soft (CQROFS) information which is the modification or generation of the complex Pythagorean and complex intuitionistic fuzzy soft sets. Some specific operational laws are also derived for the proposed work based on algebraic t-norm and t-conorm. Additionally, we also develop the Einstein’s operational laws in the presence of the CQROFS set. Consequently, based on the Einstein operational laws and CQROFS information, we derive the CQROFS Einstein weighted geometric (CQROFSEWG), CQROFS Einstein ordered weighted geometric (CQROFSEOWG), and CQROFS Einstein hybrid geometric (CQROFSEHG) operators. Some notable properties and valuable results are also explored. Moreover, we develop a multi-attribute decision-making (MADM) method based on the derived operators for CQROFS set. Finally, we do a comparative analysis between the proposed work and some existing operators to show the advantages and supremacy of the developed method.