Some aggregation operators of parameterized single-valued neutrosophic numbers and their MADM approach in simplified neutrosophic indeterminate scenarios

Abstract

Simplified neutrosophic indeterminate sets/numbers (SNISs/SNINs) can conveniently express the partially determinate and partially indeterminate information of truth, falsity, indeterminacy membership degrees, which shows its main merit. Then, the existing aggregation algorithms of SNINs lack a parameterized aggregation method to reach a flexible decision-making method subject to different decision risks. Therefore, this study proposed a MADM approach using some aggregation operators of parameterized single-valued neutrosophic numbers in a simplified neutrosophic indeterminate scenario. First, we presented a conversion technique from SNINs to parameterized single-valued neutrosophic numbers (PSVNNs) by an indeterminate parameter. Second, we proposed the score function of PSVNN and the parameterized single-valued neutrosophic weighted arithmetic averaging (PSVNWAA) and parameterized single-valued neutrosophic weighted geometric averaging (PSVNWGA) operators. Third, a multiple attribute decision-making (MADM) approach with the smaller, moderate and larger decision risks is developed by the PSVNWAA or PSVNWGA operator in a SNIS setting. Forth, the developed MADM approach is applied to the choice problem of clinical physicians as a numerical example. Generally, the developed MADM approach reveals the advantage of flexible decision making subject to the smaller, moderate, and larger decision risks of decision makers in a neutrosophic indeterminate scenario. However, this study reveals the main contributions in the aggregation algorithms of PSVNNs and flexible MADM approach in a SNIS setting.