基于Vague集的TOPSIS方法及其应用

Research on TOPSIS Methods Based on Vague Set Theory

逼近理想解的排序方法(TOPSIS)是求解多属性决策问题的一个典型方法,将TOPSIS方法在V ague集下进行了扩展。介绍了V ague集的概念及其相似度量方法,提出了用V ague值表示的语言术语集。根据V ague值的优势函数定义了V ague正、负理想解。根据V ague值的相似度量定义了各方案到正理想解和负理想解的距离,得出各方案的相对贴近度,并据此排序,供决策者选择最优方案。

TOPSIS method is a classical method to solve multiattribute decision-making problem. TOPSIS method model under Vague set theory is proposed in this paper. Firstly, the concept and similarity measure methods of Vague set are introduced, and also linguistic terms which are expressed in Vague values is presented. Secondly, based on the superiority function of Vague values, Vague positive ideal solution （VPIS） and Vague negative-ideal solution （VNIS） are defined. Thirdly, owing to the similarity measure, a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the VPIS and VNIS simultaneously, so the decision-maker can choose the optimum alternative.