Some aggregation operators of Q-neutrosophic cubic sets for multi-attribute decision making

Abstract

A neutrosophic cubic set (NCS) can depict single-valued and interval neutrosophic information simultaneously in real life. Then, the NCS concept cannot describe neutrosophic cubic information regarding the assessment problems of two-dimensional universal sets (TDUSs), while a Q-neutrosophic set (Q-NS) can depict neutrosophic information in TDUSs but not describe neutrosophic cubic information in TDUSs. Motivated by the Q-NS and NCS concepts, we need to extend the Q-NS concept to Q-NCS for indicating neutrosophic cubic information in TDUSs. Therefore, this study first proposes a Q-NCS concept, which indicates its truth, falsity, and indeterminacy values independently in TDUSs, and then the basic operations of Q-neutrosophic cubic elements (Q-NCEs) and some weighted aggregation operators of Q-NCEs, such as a Q-NCE weighted arithmetic averaging (Q-NCEWAA) operator and a Q-NCE weighted geometric averaging (Q-NCEWGA) operator. Next, Q-neutrosophic cubic multi-attribute decision-making (MADM) methods regarding the proposed Q-NCEWAA and Q-NCEWGA operators are proposed under TDUSs and Q-NCS setting. Eventually, an illustrative example shows the applicability of the proposed MADM methods in TDUSs and Q-NCS setting.