RETRACTION:Proportional intuitionistic fuzzy CODAS method: Cloud service provider selection application

Intuitionistic fuzzy sets aims at taking the hesitancy of an expert into account in assigning a membership degree or a non-membership degree. The direct assignment of decimal numbers for membership and non-membership degrees of an element in intuitionistic fuzzy sets is not practical. Besides, the assigned degrees are generally composed of one digit or at most two digits after dot. This problem has not been addressed as much as it deserves in the literature. The hypothesis of the paper is that the determination of proportional relationships between membership and non-membership degrees is more appropriate than the direct assignment to obtain the degrees. Proportional intuitionistic fuzzy (PIF) sets require only the proportion relations between an intuitionistic fuzzy set's parameters. The accuracy of the results obtained with multi-criteria decision-making models definitely depends on how accurately the membership degrees are determined. In this paper, we extend Combinative distance-based assessment (CODAS) method by using single-valued proportional intuitionistic fuzzy sets. We compare the proposed PIF CODAS method with ordinary fuzzy CODAS method. A cloud service provider selection problem is handled to show the validity of the proposed PIF CODAS method. Additionally, a comparative analysis and a sensitivity analysis together with a discussion are presented.