Distance measures for cubic Pythagorean fuzzy sets and its applications to multicriteria decision making

The main objective of this paper is to develop a sophisticated mathematical expression which can carry much more information than the general intuitionistic fuzzy set (IFS), interval-valued intuitionistic fuzzy set (IVIFS) and cubic intuitionistic fuzzy set (CIFS). CIFS is one of the powerful tools to handle uncertainty in complex situation. It is the simultaneous consideration of both the IVIFS and IFS. As in many real life situation, interval-valued Pythagorean fuzzy set (IVPFS) and Pythagorean fuzzy set (PFS) are more capable than IVIFS and IFS to represent the vagueness or ill-defined information; therefore, it motivates us to enhance the capability of CIFS in complex decision-making problems. This paper presents a novel notion of cubic Pythagorean fuzzy set (CPFS) incorporating IVPFS and PFS simultaneously, to encounter uncertainty in a more specific manner. Furthermore, a family of distance measures for CPFSs is defined and applications of the proposed distance measures are shown in medical decision-making problem.