Archimedean Aggregation Operators Based on Complex Pythagorean Fuzzy Sets Using Confidence Levels and Their Application in Decision Making

Abstract

The diagnosed complex Pythagorean fuzzy (CPF) set is a more valuable and dominant tool than the Pythagorean and intuitionistic fuzzy sets to describe awkward and unreliable information more effectively. Further, Archimedean t-norm and t-conorm have a significant influence to depict the relation among aggregated values. To take advantage of the CPF set and Archimedean t-norm and t-conorm, and assume the relation among Archimedean norms and algebraic, Einstein, Hamacher, and frank norms at the same time, in this analysis, first, we proposed the fundamental Archimedean operational laws. Second, based on these laws, we developed confidence CPF Archimedean-weighted averaging (CCPFSAWA), confidence CPF Archimedean-ordered weighted averaging (CCPFSAOWA), confidence CPF Archimedean-weighted geometric (CCPFSAWG), confidence CPF Archimedean-ordered weighted geometric (CCPFSAOWG) operators and implemented their valuable results and properties. We know that Archimedean t-norm and t-conorm are the general form of the all-aggregation operators, so by using different values of t-norm and t-conorm, we explored the confidence CPF-weighted averaging (CCPFWA), confidence CPF-ordered weighted averaging (CCPFOWA), confidence CPF Einstein-weighted averaging (CCPFEWA), confidence CPF Einstein-ordered weighted averaging (CCPFEOWA), confidence CPF Hamacher-weighted averaging (CCPFHWA), confidence CPF Hamacher-ordered weighted averaging (CCPFHOWA), confidence CPF frank-weighted averaging (CCPFFWA), confidence CPF frank-ordered weighted averaging (CCPFFOWA), confidence CPF-weighted geometric (CCPFWG), confidence CPF-ordered weighted geometric (CCPFOWG), confidence CPF Einstein-weighted geometric (CCPFEWG), confidence CPF Einstein-ordered weighted geometric (CCPFEOWG), confidence CPF Hamacher-weighted geometric (CCPFHWG), confidence CPF Hamacher-ordered weighted geometric (CCPFHOWG), confidence CPF frank-weighted geometric (CCPFFWG), and confidence CPF frank-ordered weighted geometric (CCPFFOWG) operators. Then, we developed a multi-attribute decision-making (MADM) method based on the proposed operators. Finally, many examples are used to do comparative analysis among proposed and existing methods to show the validation of the new approaches.

Balanced-Scorecard-Based Evaluation of Knowledge-Oriented Competencies of Distributed Energy Investments

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