Entropy measure and TOPSIS method based on correlation coefficient using complex q-rung orthopair fuzzy information and its application to multi-attribute decision making

Entropy measure (EM) and similarity measure (SM) are important techniques in the environment of fuzzy set (FS) theory to resolve the similarity between two objects. The q-rung orthopair FS (q-ROFS) and complex FS are new extensions of FS theory and have been widely used in various fields. In this article, the EM, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) based on the correlation coefficient is investigated. It is very important to study the SM of Cq-ROFS. Then, the established approaches and the existing drawbacks are compared by an example, and it is verified that the explored work can distinguish highly similar but inconsistent Cq-ROFS. Finally, to examine the reliability and feasibility of the new approaches, we illustrate an example using the TOPSIS method based on Cq-ROFS to manage a case related to the selection of firewall productions, and then, a situation concerning the security evaluation of computer systems is given to conduct the comparative analysis between the established TOPSIS method based on Cq-ROFS and previous decision-making methods for validating the advantages of the established work by comparing them with the other existing drawbacks.