Discriminant analysis using fuzzy linear programming models

Although powerful for the resolution of the classification problems, the major disadvantage of the parametric procedures (Linear Discriminant Function (LDF), Quadratic Discriminant Function (QDF) and Logistic Regression) is their requirement of certain assumptions. These assumptions are normality, equality of variance–covariances matrix, the absence of outliers, etc. To fill this insufficiency, several researchers such as Freed and Glover in 1980, were interested in the resolution of the classification problems via linear programming approaches. Nevertheless, the two above mentioned approaches suppose that the variables (or attributes) are measured with certainty. However, in an increasingly complex environment, these variables can be imprecise, qualitative or linguistic. In such a case, fuzzy set theory seems to be the convenient tool to fill this insufficiency. Thus, we proposed a new approach, which consists in solving the classification problems via Fuzzy Linear Programming Models (FLPM).