Development of a Reduced Fuzzy Soft Set Mathematical Framework for Transforming Fuzzified Acoustic Voice Data into Parameterized Diagnostic Structures

Abstract

This paper analyses the development of a reduced fuzzy soft mathematical framework for modelling and detecting vocal disorder risk using clinical data. The paper presents a mathematically grounded fuzzy soft expert system for the quantitative assessment of vocal disorder risk based on acoustic and demographic parameters. Let = { denote a finite universe of patients and denote the parameter set comprising fundamental frequency, vocal perturbation index, and age. Clinical acoustic data were collected and represented as a dataset  Linguistic variables were obtained by the process of fuzzification using the appropriate designed membership functions assessment model.  For each, a fuzzy membership function  is constructed using continuous triangular membership function to represent linguistic classifications. The fuzzified linguistic variables were further transformed into soft set using discrete α-cut levels. Discrete α-cut levels are employed to generate parameterized soft sets, which are subsequently reduced using redundancy elimination criteria derived from soft set theory. The reduced parameter sets preserve essential diagnostic information while minimizing computational complexity. The resulting mathematical framework provides a systematic method for organizing acoustic information without enforcing binary classification. The mathematical formulation preserves uncertainty, enables modelling of multiple parameter interaction and prepares the dataset for advanced diagnostic inference. The mathematically technique is consistent, scalable, and suitable for biomedical applications involving imprecise data.