Multiple attribute decision making based on immediate probabilities aggregation operators for single-valued and interval neutrosophic sets

The objective of this paper is to present novel algorithms for solving the multiple attribute decision-making problems under the neutrosophic set environment. Single-valued and interval neutrosophic sets are the important mechanisms for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Also, to describe the behavior of the decision-maker objectively (in terms of probability) and subjectively (in terms of weights), a concept of probabilistic information plays a dominant role in the investigation. Keeping these features in mind, this paper presents several probabilistic and immediate probability-based averaging and geometric aggregation operators for the collection of the single-valued and interval neutrosophic sets. The advantage of these proposed operators is that it simultaneously combines the objective and subjective behavior of the decision-maker during the process. The various salient features of the proposed operators are studied. Later, we develop two new algorithms based on the aggregation operators to solve multiple attribute decision-making problems with single-valued and interval neutrosophic sets features. A numerical example related to the demonetization is given to demonstrate the presented approaches, and the advantages, as well as comparative analysis, are given to shows its influence over existing approaches.