Extension of Intersection Method for Multi-Objective Optimization in Case of Interval Number and its Application

This paper aims to develop the extension of intersection method for multi-objective optimization under condition of interval number. Based on the linear correlation of partial favourable probability and the corresponding performance indicator, and the assumption of uniform distribution of the actual value of performance indicator within the range of its lower and upper limits in case of interval number, it derives that the actual partial favourable probability of a performance indicator is the arithmetic mean value of the partial favourable probabilities of the arithmetic mean value and the variation value of the interval index of the corresponding performance indicator for each candidate, or their desired sum. Furthermore, according to the rule of algorithm for the total favourable probability quantitatively, all candidates are ranked according to their total favourable probabilities to complete the multi- objective optimization in case of interval number. As applications, the quantitative assessments of multi-criteria selections for effective dwelling house walls, project managers and contractor for construction works are given in detail, satisfied results are obtained.