Similarity measure for complex non-linear Diophantine fuzzy hypersoft set and its application in pattern recognition

As a hybrid fuzzy extension of the complex non-linear Diophantine fuzzy set, the complex nonlinear Diophantine fuzzy hypersoft set was developed by fusing it with the hypersoft set. To address multi-sub-attributed real-world similarity problems within complex non-linear Diophantine fuzzy ambiance, this study proposes distance measures and five innovative similarity measures such as Jaccard similarity measure, exponential similarity measure, cosine similarity measure, similarity measure based on cos function, and similarity measure based on cot function for complex nonlinear Diophantine fuzzy hypersoft set. Furthermore, based on proposed similarity measures, a highly effective algorithm is provided for handling decision-making issues exquisitely in the pattern recognition field, along with an illustrative example of mineral identification. Then, to demonstrate the validity, reliability, robustness, and superiority of the proposed notion and algorithm, a detailed comparative study with proper discussion has been presented in the study.