Einstein Aggregation Operators of Simplified Neutrosophic Indeterminate Elements and Their Decision-Making Method

Abstract

Since current decision problems are becoming more and more complex, the decision environment is becoming more and more uncertain. The simplified neutrosophic indeterminate element (SNIE) was defined to adapt to the expression of the indeterminate and inconsistent information in the indeterminate decision-making problems. SNIE consists of the truth, indeterminacy, and falsity neutrosophic numbers and can express a singled value neutrosophic element or an interval value neutrosophic element depending on the value/range of indeterminacy. In this article, we first define some operational rules of SNIEs based on the Einstein T-norm and T-conorm. Next, SNIE Einstein weighted averaging (SNIEEWA) and SNIE Einstein weighted geometric (SNIEEWG) operators are proposed to aggregate SNIEs. In view of the SNIEEWA and SNIEEWG operators, a multi-attribute decision-making (MADM) method is proposed in the case of SNIEs. Finally, the proposed MADM method is applied to solve indeterminate MADM problems in the case of SNIEs. Furthermore, the validity and effectiveness of the proposed method are verified through an illustrative example and comparative analysis.