Fan Zhi-Ping, Liu Yang
Department of Management Science and Engineering, School of Business Administration, Northeastern University, Shenyang 110004, China.
IEEE Trans Syst Man Cybern B Cybern. 2010 Oct;40(5):1413-23. doi: 10.1109/TSMCB.2009.2039477. Epub 2010 Feb 17.
The ordinal interval number is a form of uncertain preference information in group decision making (GDM), while it is seldom discussed in the existing research. This paper investigates how the ranking order of alternatives is determined based on preference information of ordinal interval numbers in GDM problems. When ranking a large quantity of ordinal interval numbers, the efficiency and accuracy of the ranking process are critical. A new approach is proposed to rank alternatives using ordinal interval numbers when every ranking ordinal in an ordinal interval number is thought to be uniformly and independently distributed in its interval. First, we give the definition of possibility degree on comparing two ordinal interval numbers and the related theory analysis. Then, to rank alternatives, by comparing multiple ordinal interval numbers, a collective expectation possibility degree matrix on pairwise comparisons of alternatives is built, and an optimization model based on this matrix is constructed. Furthermore, an algorithm is also presented to rank alternatives by solving the model. Finally, two examples are used to illustrate the use of the proposed approach.
序数区间数是群决策（GDM）中一种不确定偏好信息形式，然而现有研究中对此讨论较少。本文研究了在GDM问题中如何基于序数区间数的偏好信息确定方案的排序顺序。当对大量序数区间数进行排序时，排序过程的效率和准确性至关重要。提出了一种新方法，当认为序数区间数中的每个排序序数在其区间内均匀且独立分布时，使用序数区间数对方案进行排序。首先，给出了比较两个序数区间数时的可能度定义及相关理论分析。然后，为了对方案进行排序，通过比较多个序数区间数，构建了方案两两比较的集体期望可能度矩阵，并基于该矩阵构建了一个优化模型。此外，还提出了一种通过求解该模型对方案进行排序的算法。最后，通过两个例子说明了所提方法的使用。
