Distance and Similarity Measures on Generalized Interval-Valued Pythagorean Fuzzy Soft Sets and their Decision-making Applications in Sports

Distance and similarity measures are crucial for assessing the resemblance or divergence of information, and they are employed in image processing, pattern recognition, and clustering. The intervals are employed in mathematics to assess ambiguous data in the case of dispersed patterns. In other words, interval-valued (IV) representation gives the edge to tackle ambiguous data to yield most likely outcomes. The generalized IV Pythagorean Fuzzy Soft Set (GIVPFSS) is based on the composition of an IV Pythagorean Fuzzy Soft Set (IVPFSS) and IV Pythagorean Fuzzy Sets (IVPFSs) which serve to summarize data with respect to criteria in IVPFSS. The GIVPFSS computed information on several aspects of ambiguity in the form of IV Pythagorean fuzzy numbers. The real-world application of GIVPFSSs is indicated by how it evaluates cricket players’ skills in playing field positions. Its basic capabilities are recognized, particularly its valued form named as GIVPFSV. Afterwards, we establish distance and similarity measures on GIVPFSSs and demonstrate their fundamental characteristics. Based on similarity and distance metrics for GIVPFSSs, a multi-criteria decision-making (MCDM) system is provided. An example comprising several sports clubs is taken into consideration when evaluating the best province for sports activities. A comparison with the current primary MCDM techniques is given at the end.