On Min-Max Goal Programming Approach for Solving Piecewise Quadratic Fuzzy Multi- Objective De Novo Programming Problems

De novo programming is considered an essential tool for establishing optimal system design. This paper studies the Multi-Objective De Novo Programming (MODNP) problem with Piecewise Quadratic Fuzzy (PQF) data in the objective function coefficients. One of the best interval approximations, namely, the close interval approximation of the PQF number, is applied to solve the MODNP problem. A necessary and sufficient condition for the solution from the efficiency standpoint is established. A Min-max goal programming approach with positive and negative ideals is proposed to obtain optimal compromise system design. The stability set of the first kind corresponding to the optimal system design is defined and determined. The stability set of the first kind corresponding to the optimal system design is determined. The steps of the proposed solution approach are illustrated through numerical examples.