Nonparametric statistical hypothesis testing in soft set theory

Abstract

Theories of uncertainty plays a vital role in decision making. Efforts are being made in combining statistical hypothesis testing methods with uncertainty theories having membership and nonmembership values. Soft set theory was developed as a generalization of fuzzy set theory to avoid having difficulties in assigning membership values. In this paper, an attempt is made to impose statistical hypothesis testing methods in soft set theory to handle decision making problems with linguistic data. For this purpose, non-normality of the data has been analyzed by using Shapiro Wilk test for normality following which Skillings Mack nonparametric test has been computed in soft data using chi-squared distribution and Monte Carlo method. To demonstrate this, significance difference in the sample data set of manpower positions (Radiographers, pharmacists, lab technician, nurses and specialty doctors) in the community health centers in Southern states of India from 2019 to 2022 has been computed. Tools used: R