Subtraction operational aggregation operators of simplified neutrosophic numbers and their multi-attribute decision making approach

Abstract

The simplified form of a neutrosophic set (NS) was introduced as the simplified NS (S-NS) containing an interval-valued NS (IV-NS) and a single-valued NS (SV-NS) when its truth, indeterminacy and falsity membership degrees are constrained in the real standard interval [0, 1] for the convenience of actual applications. Then, Ye presented subtraction operations of simplified neutrosophic numbers (S-NNs), containing the subtraction operations of interval-valued neutrosophic numbers (IV-NNs) and single-valued neutrosophic numbers (SV-NNs) in S-NN setting. However, the subtraction operations of S-NSs lack actual applications in current research. Since simplified neutrosophic aggregation operators are one of critical mathematical tools in decision making (DM) applications, they have been not investigated so far. Regarding the subtraction operations of S-NNs (SV-NNs and IV-NNs), this work proposes an IV-NN subtraction operational weighted arithmetic averaging (IV-NNSOWAA) operator and a SV-NN subtraction operational weighted arithmetic averaging (SV-NNSOWAA) operator as a necessary complement to existing aggregation operators of S-NNs to aggregate S-NNs (SV-NNs and IV-NNs). Then, a DM approach is developed by means of the SV-NNSOWAA and IV-NNSOWAA operators. Finally, an illustrative example is presented to indicate the applicability and effectiveness of the developed approach.