Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information

The Choquet integral is a fuzzy measure that serves as an effective aggregation operator for combining a limited number of components into a single set. In 1978, Hamacher introduced the Hamacher t-norm and t-conorm, an expanded version of algebraic t-norms. In this article, we present the aggregation operators for the Choquet integral that utilize the Hamacher t-norms to handle the theory of complex intuitionistic fuzzy values. These operators include the complex intuitionistic fuzzy Hamacher Choquet integral averaging and geometric operators. Additionally, an analysis is conducted on the attributes and special situations of the suggested methodologies. In addition, a novel approach is presented, utilizing newly developed operators for solving multi-attribute decision-making issues with complex intuitionistic fuzzy values. The operational stages of this strategy are thoroughly presented. Finally, we conducted a comprehensive comparison between the proposed methodology and existing approaches, using illustrative examples to validate the effectiveness and demonstrate the advantages of the proposed methods.