The Aggregation Operators Based on Archimedean t-Conorm and t-Norm for Single-Valued Neutrosophic Numbers and their Application to Decision Making

Abstract

The single-valued neutrosophic set (SVNS) can be easier to describe the incomplete, indeterminate and inconsistent information, and Archimedean t-conorm and t-norm (ATT) can generalize most of the existing t-conorms and t-norms, including Algebraic, Einstein, and Hamacher Frank t-conorms and t-norms. In this paper, we extended ATT to the single-valued neutrosophic numbers (SVNNs), and proposed a single-valued neutrosophic number-weighted averaging (SVNNWA) operator and a single-valued neutrosophic number-weighted geometric (SVNNWG) operator based on ATT. First, we presented some new operational laws for SVNNs based on ATT, and discussed some special cases and properties of them. Then we proposed the SVNNWA and SVNNWG operators, and studied some properties and special cases of them. Further, we gave the decision-making methods for multiple attribute decision-making (MADM) and multiple attribute group decision-making (MAGDM) problems based on these operators. Finally, two examples are given to verify the developed approaches.