In our daily lives, the number and variety of uncertainty problems we encounter in fields such as engineering, health, economics and law are increasing. Highly effective methods are being produced to cope with uncertainties. Hybrid versions of fuzzy sets and their derivatives and soft sets especially give very successful results in this regard. In this study, we introduce fuzzy parameterized cube root fuzzy (CR-fuzzy) soft set, a new hybrid set, and give some set operations. These sets are quite successful in decision-making processes. It will make a significant contribution, especially in solving multi-criteria decision-making problems.