A New Interval Comparison Relation and Application in Interval Number Programming for Uncertain Problems

For optimization or decision-making problems with interval uncertainty, the interval comparison relation plays a very important role, as only based on it a better or best decision can be determined. In this paper, a new kind of interval comparison relation termed as reliability-based possibility degree of interval is proposed to give quantitative evaluations on “how much better” of one interval than another, which is more suitable for engineering reliability analysis and numerical computation than the existing relations. In the new relation, the range of the comparing values is extended into the whole real number field, and the precise comparison is made possible for any pairs of intervals on the real line. Furthermore, the suggested interval comparison relation is applied to the interval number programming, and two kinds of transformation models are developed for both of the linear and nonlinear interval number programming problems, based on which the uncertain optimization problems can be changed into traditional deterministic optimization problems. Two numerical examples are finally investigated to demonstrate the effectiveness of the two transformation models.