Table 1 Comparison of key studies and our proposed approach.

Dhumras et al.³²

Novel SM for CPFS

Pattern Recognition

Focuses on pattern recognition; current study combines SM and DM for CPFS in TOPSIS applied to speech and sports training

Dhumras et al.³³

Modified TOPSIS with R-norm q-rung Picture Fuzzy Information Measure

Green Supplier Selection

Applies to supplier selection; current study applies SM and DM for CPFS in decision-making for speech and sports

Singh et al.³⁴

Modified TOPSIS with R-norm Picture Fuzzy Discriminant Measure

Green Supplier Selection

Focuses on green supplier selection; current study applies CPFS-TOPSIS to speech and sports applications

Dhumras et al.³⁵

q-Rung Picture Fuzzy TOPSIS/VIKOR in Federated Learning

Electronic Marketing

Uses federated learning and marketing; current study applies CPFS-TOPSIS to real-world speech and sports data

Sharma et al.³⁶

Picture Fuzzy Discriminant Measure

Banking Site Selection

Focuses on banking site selection; current study applies CPFS-TOPSIS to speech matching and sports training feature recognition

CPF-IM TOPSIS (Proposed)

Introduces SM and DM for CPFS, integrated into the TOPSIS method

Speech Matching and Sports Training Feature Recognition

Unlike existing models, the proposed approach addresses uncertainty and Cyclicity effectively, incorporating real and imaginary components in CPFS to improve decision-making under complex uncertainty, a gap not fully addressed in prior studies