Among various statistical and data mining discriminant analysis proposed so far for group classification, linear PROGRAMMING discriminant analysis has recently attracted the researchers’ interest. This study evaluates multi-group discriminant linear PROGRAMMING (MDLP) for classification problems against well-known methods such as neural networks and support vector machine. MDLP is less complicated as compared to other methods and does not suffer from having local optima. This study also proposes a fuzzy Delphi method to select and gather the required data, when databases suffer from deficient data. In addition, to absorb the uncertainty infused to collecting data, INTERVAL MDLP (IMDLP) is developed. The results show that the performance of MDLP and specially IMDLP is better than conventional classification methods with respect to correct classification, at least for small and medium-size datasets.

In this paper, an INTERVAL fractional optimization problem with directionally differentiable functions is considered, and the d-invexity concept is introduced for INTERVAL-valued functions. Slater's constraint qualification and pre-invex directional derivative assumption are used to establish the necessary optimality conditions. Further, sufficient optimality conditions are derived under the d-invexity assumption, considering the LU-solution concept. As an application of INTERVAL fractional problems, a portfolio optimization problem with uncertain return and risk parameters subject to INTERVAL liquidity constraints is considered, and an optimal solution is obtained using the results developed in this paper. Also, the portfolio optimization problem is solved using the proposed global criteria method for INTERVAL optimization problems and two methods available in the literature. Moreover, to check the efficiency of the proposed method, a comparison between different methods is presented. Throughout the paper, non-trivial examples are presented at appropriate places to provide a better understanding of the results developed.