An Innovative Decision-Making Approach Based on Correlation Coefficients of Complex Picture Fuzzy Sets and Their Applications in Cluster Analysis.

In modern times, the organizational managements greatly depend on decision-making (DM). DM is considered the management's fundamental function that helps the businesses and organizations to accomplish their targets. Several techniques and processes are proposed for the efficient DM. Sometimes, the situations are unclear and several factors make the process of DM uncertain. Fuzzy set theory has numerous tools to tackle such tentative and uncertain events. The complex picture fuzzy set (CPFS) is a super powerful fuzzy-based structure to cope with the various types of uncertainties. In this article, an innovative DM algorithm is designed which runs for several types of fuzzy information. In addition, a number of new notions are defined which act as the building blocks for the proposed algorithm, such as information energy of a CPFS, correlation between CPFSs, correlation coefficient of CPFSs, matrix of correlation coefficients, and composition of these matrices. Furthermore, some useful results and properties of the novel definitions have been presented. As an illustration, the proposed algorithm is applied to a clustering problem where a company intends to classify its products on the basis of features. Moreover, some experiments are performed for the purpose of comparison. Finally, a comprehensive analysis of the experimental results has been carried out, and the proposed technique is validated.

Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function.

In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev's inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent k-hypergeometric function.