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.