Possibility-induced simplified neutrosophic aggregation operators and their application to multi-criteria group decision-making

Abstract

Simplified neutrosophic set (SNS) is an appropriate tool used to express the incompleteness, indeterminacy and uncertainty of the evaluation objects in decision-making process. In this study, we define the concept of possibility SNS including two types of information such as the neutrosophic performance provided from the evaluation objects and its possibility degree using a value ranging from zero to one. Then by extending the existing neutrosophic information, aggregation models for SNSs that cannot be used effectively to fusion the two different information described above, we propose two novel neutrosophic aggregation operators considering possibility, which are named as a possibility-induced simplified neutrosophic weighted arithmetic averaging operator and possibility-induced simplified neutrosophic weighted geometric averaging operator, and discuss their properties. Moreover, we develop a useful method based on the proposed aggregation operators for solving a multi-criteria group decision-making problem with the possibility simplified neutrosophic information, in which the weights of decision-makers and decision criteria are calculated based on entropy measure. Finally, a practical example is utilised to show the practicality and effectiveness of the proposed method.

Keywords:

• Neutrosophic sets
• simplified neutrosophic sets
• multi-criteria group decision-making
• possibility simplified neutrosophic sets

Acknowledgments

The authors would like to thank the editors and the anonymous referees for their valuable and constructive comments and suggestions that greatly helped the improvement of this paper.