A Parametric Similarity Measure for Spherical Fuzzy Sets and Its Applications in Medical Equipment Selection

The Spherical Fuzzy Set (SFS) framework extends the Picture Fuzzy Set (PFS) concept, offering enhanced precision in handling data characterized by conflict and uncertainty. Furthermore, similarity measures (SMs) are crucial for determining the extent of resemblance between pairs of fuzzy values. While existing SMs evaluate similarity by measuring the distance between values, they sometimes yield results that are illogical or unreasonable, due to certain properties and operational complexities. To address these anomalies, this paper introduces a parametric similarity measure based on three adjustable parameters (α₁, α₂, α₃), allowing decision-makers to fine-tune the measure to suit various decision-making styles. This paper also scrutinizes existing SMs from a mathematical standpoint and demonstrates the efficacy of the proposed SM through mathematical modeling. Finally, we apply the proposed SM to tackle Multi-Attribute Decision-Making (MADM) problems. Comparative analysis reveals that our proposed SM outperforms certain existing SMs in the context of SFS-based applications.