Fuzzy Discriminant Analysis with Application

In the current research, two methods of data classification were used, namely; the Linear Discriminant analysis (LDA) and the Fuzzy Discriminant Analysis (FDA). The discriminant analysis is considered as a method in which a certain item is analyzed into one of the sets depending on statistically significant variables in the process of analysis. The item is classified within the suitable population through a set of variables. Sometimes, the data is non-linear or does not follow a normal distribution or is unstable, so the use of fuzzy logic is successful because it does not require the data to follow a normal distribution or to be stable and Through fuzzy theory, models are developed to solve problems that cannot be analyzed using pure mathematical methods. The research aims to compare the two analysis methods (LDA) and (FDA) in order to display data and distinguish between different categories with high accuracy, provide accurate classifications of observations, as well as diagnose variables of high importance in discriminatory data using confidence intervals for the Roy-Bose test and the t-test. Real data was used for two groups of kidney patients (infected, not infected) depending on a set of influencing factors and the extent to which each factor affects the persons or the new items and their distribution on one of the two sets, which in turn, leads to early diagnosis and avoiding the deterioration of the  health state of the patient. Results were obtained after applying the statistical package (SPSS) and (R) statistical package, which indicated that the fuzzy discriminant analysis (FDA) was the best analysis as it yields the least classification error by depending on the mean standard error (MSE).