The notion of trigonometric similarity measures (SMs) for spherical fuzzy sets has become very important in solving various problems in pattern recognition and medical diagnosis. This study proposes some trigonometric SMs with the help of Choquet integral (CI) for spherical fuzzy sets. The proposed trigonometric SMs clearly satisfy the axiomatic definition of classical SMs. We also perform these SMs in pattern recognition problems to examine a comparative analysis of the proposed trigonometric SMs with some existing SMs. Spearman's rank correlation coefficient is utilized to demonstrate the effectiveness of the proposed SMs.

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We introduce a new concept for multivalued maps, also called multivalued nonlinear F-contraction, and give a fixed point result. Our result is a proper generalization of some recent fixed point theorems including the famous theorem of Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334(1):132–139, 2007].

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In the present paper, considering the simulation function, we give a new class of Picard operators on complete metric spaces. We also provide a nontrivial example that shows the aforementioned class properly contains some earlier such classes.