Affiliations: Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, Turkey
Correspondence:
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Corresponding author. Mesut Karabacak, Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, Turkey. E-mail: mkarabacak@atauni.edu.tr.
Abstract: The correlation coefficient (CC) is a well-known functional information measures used to measure the interrelationship between uncertain, fuzzy sets. The use of neutrosophic sets (NS) in decision making has been increasing in recent times. Many studies have been considered to calculate the CC of NSs. These approaches assess only the strength of relationship between PNSs, and are described within the interval [0, 1]. However, the inclusion of the reliability level of the data in the process is very important for the final decision. Therefore, neutrosophic Z-Number sets (NZNS) has been defined for this purpose, which are not only provide an assessment of the data but also take into account their confidence level. In this study, we define a correlation coefficient for NZNSs (CCNZNS) by employing the notions of mean, variance and covariance, and discuss some of its properties. This new approach defines correlation in the interval [–1, 1] similar to classical statistics, and indicates whether the NZNSs are either positively or negatively correlated. Then, two decision models are developed for the NZNS universe. In order to determine the partial known attribute weights, a maximizing optimization technique is derived which is taking into account both the objective and subjective aspects of assessments. To demonstrate the effectiveness of the proposed models, the first model is applied for solving a medical diagnostic problem. Then the performance evaluation process is chosen to demonstrate the application of the second model. Finally, the superior aspects of the developed models over other existing models are presented with a comparison and discussion analysis. The study is concluded with the conclusion part.
Keywords: Neutrosophic Z-number set, correlation coefficient, variance, covariance, decision making
