Generalized Heronian Mean Operators Based on Archimedean T-Norms of the Complex Picture Fuzzy Information and Their Application to Decision-Making

Abstract

Complex picture fuzzy set is a special picture fuzzy set where the truth, abstinence, and falsity grades are shown by a complex number and can effortlessly illustrate the problem and inconsistency in the genuine world. T-norm and t-conorm play an essential and beneficial role in the environment of fuzzy set theory; similarly, Archimedean t-norm and t-conorm have massive flexibility and dominancy in the information fusion procedure. The major contribution of this analysis is to explore the algebraic, Einstein, Hamacher, and Frank operational laws under the complex picture fuzzy set. Moreover, the principle of complex picture fuzzy Archimedean Heronian aggregation operator and complex picture fuzzy weighted Archimedean Heronian aggregation operator are also elaborated by using Archimedean t-norm and t-conorm. Additionally, by using the elaborated operators, a multiattribute decision-making technique is presented to elaborate the consistency and reliability of the explored works. Finally, many examples are illustrated for discussing the advantages and sensitive analysis and graphical representation of the investigated works.