Spherical fuzzy sets (SFSs) have gained great attention from researchers in various fields. The spherical fuzzy set is characterized by three membership functions expressing the degrees of membership, non-membership and the indeterminacy to provide a larger preference domain. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and vagueness information. The similarity measure is one of the essential and advantageous tools to determine the degree of similarity between items. Several studies on similarity measures have been developed due to the importance of similarity measure and application in decision making, data mining, medical diagnosis, and pattern recognition in the literature. The contribution of this study is to present some novel spherical fuzzy similarity measures. We develop the Jaccard, exponential, and square root cosine similarity measures under spherical fuzzy environment. Each of these similarity measures is analyzed with respect to decision-makers' optimistic or pessimistic point of views. Then, we apply these similarity measures to medical diagnose and green supplier selection problems. These similarity measures can be computed easily and they can express the dependability similarity relation apparently.