MAGDM Model Using the Aczel-Alsina Aggregation Operators of Neutrosophic Entropy Elements in the Case of Neutrosophic Multi-Valued Sets

Abstract

To overcome the limitations of both the conversion method based on the standard deviation and the decision flexibility in existing neutrosophic multi-valued decision-making models, this study aims to propose various new techniques including a conversion method, Aczel-Alsina aggregation operations, and a multi-attribute group decision making (MAGDM) model in the case of neutrosophic multi-valued sets (MVNSs). First, we propose a conversion method to convert neutrosophic multi-valued elements (MVNEs) into neutrosophic entropy elements (NEEs) based on the mean and normalized Shannon/probability entropy of truth, falsity, and indeterminacy sequences. Second, the score and accuracy functions of NEEs are defined for the ranking of NEEs. Third, the Aczel-Alsina t-norm and t-conorm operations of NEEs and the NEE Aczel-Alsina weighted arithmetic averaging (NEEAAWAA) and NEE Aczel-Alsina weighted geometric averaging (NEEAAWGA) operators are presented to reach the advantage of flexible operations by an adjustable parameter. Fourth, we propose a MAGDM model in light of the NEEAAWAA and NEEAAWGA operators and the score and accuracy functions in the case of NMVSs to solve flexible MAGDM problems with an adjustable parameter subject to decision makers’ preference. Finally, an illustrative example is given to verify the impact of different parameter values on the decision results of the proposed MAGDM model. Compared with existing techniques, the new techniques not only overcome the defects of existing techniques but also be broader and more versatile than existing techniques when dealing with MAGDM problems in the case of NMVSs.

Keywords

• neutrosophic multi-valued set
• neutrosophic entropy element