This paper presents a new correlation coefficient measure, which satisfies the requirement of this measure equaling one if and only if two interval neutrosophic sets (INSs) are the same. And an objective weight of INSs is presented to unearth and utilize deeper information that is uncertain. Using the proposed weighted correlation coefficient measure of INSs, a decision-making method is developed, which takes into account the influence of the evaluations' uncertainty and both the objective and subjective weights.

Decision support is a vital function in electronic commerce (e-commerce). The purpose of this paper is to construct a review-based decision support model for items comparison in e-commerce. The proposed model uses probability multivalued neutrosophic linguistic numbers (PMVNLNs) to characterize online reviews. It overcomes the limitation of existing models by considering neutral information and hesitancy in text reviews. The fuzzy characterization of reviews (i.e., PMVNLN) can reflect similarities and differences in positive (negative) information. In addition, the model considers consumers' bounded rational behaviors by combining the regret theory with an outranking method. We empirically compare the proposed model with models in PConline.com and four existing models with data from PConline.com. The performance of these models in terms of accuracy is measured by the total relative difference metric. Results indicate the good performance of the proposed model. Our model is a promising option for e-commerce to provide consumers with good decision support service.

Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decision-making problems. Preference relations represent a practical tool for presenting decision makers’ preference information regarding various alternatives. The purpose of this paper is to propose single-valued trapezoidal neutrosophic preference relations (SVTNPRs) as a strategy for tackling multi-criteria decision-making problems. First, this paper briefly reviews basic concepts about neutrosophic sets and SVTNNs and defines a new comparison method and new operations for SVTNNs. Next, two aggregation operators, the single-valued trapezoidal neutrosophic weighted arithmetic average operator and the single-valued trapezoidal neutrosophic weighted geometric average operator, are proposed for applications in information fusion. Then, this paper discusses the definitions of completely consistent SVTNPRs and acceptably consistent SVTNPRs. Finally, we outline a decision-making method based on SVTNPRs to address green supplier selection problems, and we conduct a comparison study and discussion to illustrate the rationality and effectiveness of the decision-making method.