A solution proposal to nonlinear programming problem

The main purpose of decision making methods is to provide a holistic criterion to evaluate the utility of an action or choice based on multiple criteria. Practical and real world decision making problems often must satisfy several goals which are sometimes conflicting and inconsistent. Such a problem is the subject of multiple criteria decision making methods. Furthermore, the occurrence of randomness and imprecision in the real world is inevitable owing to some unexpected situations. Therefore, imposing the uncertainty upon the conventional optimization problems is an interesting research topic. In this paper, a new efficient structure is developed to deal with interval nonlinear multiobjective programming problems. In the first step, the proposed method applied a compromise programming based logic to obtain the best and worst solutions of each interval objectives. In the second phase, the proposed method tries to find the better compromise solution which simultaneously satisfied different objectives based on a fuzzy set approach. The rest of the paper is organized as follows. The first section provides information about literature. In section 2, the basic definitions and theorems of mathematical programming and optimality are given. The third and fourth sections provide information about fuzzy logic, fuzzy programming, interval arithmetic and interval programming. In section 5, the proposed methods are given for solving general interval nonlinear programming problems. In section 6, the proposed methods are applied to the problems. Some interesting results and proposals are presented in section 7.