Weighted aggregation operators of single-valued neutrosophic linguistic neutrosophic sets and their decision-making method

Abstract

Multiple attribute decision-making (MADM) problems often contain quantitative and qualitative information that is inconsistent, uncertain, and incomplete. However, existing evaluation methods can only perform quantitative or qualitative processing on all attribute data, which easily leads to some information loss. In order to deal with MADM problems more effectively, this paper proposes a single-valued neutrosophic linguistic neutrosophic element (SvNLNE), which consists of a single-valued neutrosophic number for quantitative expression and a linguistic neutrosophic number for qualitative description. This paper also provides the fundamental operations of SvNLNEs, the SvNLNE score and accuracy functions for sorting the elements, and the SvNLNE weighted arithmetic averaging (SvNLNEWAA) and geometric averaging (SvNLNEWGA) operators for information aggregation. Finally, some MADM approaches are developed based on the SvNLNEWAA and SvNLNEWGA operators, and their application and rationality are further illustrated by an investment case in the SvNLNE setting.

Keywords

• multi-attribute decision making
• single-valued neutrosophic linguistic neutrosophic element
• neutrosophic element weighted arithmetic averaging operator