Affiliations: [a] Department of Civil Engineering,Shaoxing University, Huancheng West Road, Shaoxing, Zhejiang Province,P.R. China | [b] Department of Electrical Engineering and Automation,Shaoxing University, Huancheng West Road, Shaoxing, Zhejiang Province,P.R. China
Correspondence:
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Corresponding author. Jun Ye, Department of Electrical Engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang Province 312000, P.R. China. Tel.: +86 575 88327323; E-mails:[email protected],[email protected]
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.
Keywords: Q-neutrosophic cubic set, two-dimensional universal sets, Q-neutrosophic cubic element weighted geometric averaging (Q-NCEWAA) operator, Q-neutrosophic cubic element weighted geometric averaging (Q-NCEWGA) operator, decision making
