Some distance measures for pythagorean cubic fuzzy sets: Application selection in optimal treatment for depression and anxiety.

Pythagorean cubic fuzzy sets represent an advancement beyond conventional interval-valued Pythagorean sets, integrating the principles of Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets. Given the critical significance of distance measures in real-world decision-making and pattern recognition tasks, it is noteworthy that there exists a notable gap in the literature regarding distance measures specifically tailored for Pythagorean cubic fuzzy sets. The objectives of this paper are:•To define novel generalized distance measures between Pythagorean cubic fuzzy sets (PCFSs) to tackle intricate decision-making challenges.•These novel distance measures are undergoing testing on a real-world scenario concerning the management of anxiety and depression to evaluate their effectiveness and practical application.•We have illustrated the boundedness and nonlinear characteristics inherent in these distance measures. In addition, we conduct comparative analyses with existing approaches to validate the proposed methodology, thereby providing insights into its advantages and potential applications.