Fuzzy optimization problems based on inequality degree

For most actual problems, especially about production-line optimization problems in complex manufacturing systems, it often needs to process integrally a large amount of different types of uncertain information with complex constraints. In this paper, we construct several types of fuzzy inequality degree in different ways, whose basic analytical properties such as continuity and monotonicity are also considered. Then we give a formula computing the inequality degree of triangular fuzzy numbers. Furthermore, using the inequality degree, we establish a mathematical model for solving uncertain optimization problems with complex constraints. Finally, through an example, we explain how to transform a fuzzy constraint and how to compute the inequality degree and process fuzzy constraint numerically.