Prioritized Aggregation Operators for Complex Intuitionistic Fuzzy Sets Based on Aczel-Alsina T-norm and T-conorm and Their Applications in Decision-Making

The Aczel-Alsina t-norms ware proposed by Aczel and Alsina in 1982, which are a very effective and dominant technique used in the construction of any kind of aggregation operators. Moreover, the Algebraic t-norms are a special case of the Aczel-Alsina t-norms because of the parameter 0<p<+∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<p<+\infty$$\end{document}. Additionally, a complex intuitionistic fuzzy (COIF) set is an essential and valuable part of the fuzzy set to handle vague and awkward situations in many real-life problems. Motivated by the above valuable and dominant ideas, the major contribution of this study is to propose the aggregation operators by involving the priority degree based on Aczel-Alsina t-norms for managing the COIF values, such as COIF Aczel-Alsina prioritized weighted averaging (COIFAAPWA), COIF Aczel-Alsina prioritized ordered weighted averaging (COIFAPOWA), COIF Aczel-Alsina prioritized weighted geometric (COIFAAPWG), and COIF Aczel-Alsina prioritized ordered weighted geometric (COIFAAPOWG) operators. The fundamental properties of these operators are also examined. Afterward, we develop a decision-making technique to process the multi-attribute decision-making (MADM) problem based on the COIF information and proposed operators. Lastly, we use some examples to show the supremacy and effectiveness of the developed approaches by checking the influence of the parameters and the comparison between proposed techniques with some existing techniques.