Generalized correlation coefficients of intuitionistic multiplicative sets and their applications to pattern recognition and clustering analysis

Intuitionistic multiplicative preference relations (IMPRs) and intuitionistic multiplicative sets (IMSs) play a significant role in real-life problems that contain unsymmetrical and nonuniform information. Correlation coefficients are critical tools for evaluating such information, especially in medical areas and clustering analysis, where the relationship between objects in the given data is required. Despite the importance of this subject, there is only one approach in the literature regarding the correlation coefficients of IMSs and existing coefficients have certain disadvantages. In this paper, we propose a parametric generalisation of these correlation coefficients on IMSs and apply them to medical diagnosis, taxonomy, and clustering. To that end, some disadvantages of existing correlation coefficients are listed first. Then, with some theoretical work, we derive a parametric generalisation of these coefficients and their weighted forms. To better illustrate how the parametric generalisation of correlation coefficients improves the results, numerical parametric solutions of existing examples are presented with detailed comparisons. Moreover, a novel algorithm is introduced for clustering using proposed correlation coefficients in IMSs. Finally, three real-life examples are provided to demonstrate the superiority of the proposed generalised correlation coefficients and the clustering algorithm in specific applications.