基于模糊数整体和局部特征的一种新排序方法  

A New Approach with the Overall Characteristics and the Partial Ones for Ranking Fuzzy Numbers

作　　者：牟琼[1] 程云龙[2] 邱东[1] 

机构地区：[1]重庆邮电大学数理学院,重庆400065 [2]重庆邮电大学移通学院,重庆400065

出　　处：《模糊系统与数学》2012年第1期91-98,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金数学天元项目(11126087);重庆市教委项目(KJ100518);重庆邮电大学青年科学基金资助项目(A2008-44);重庆邮电大学移通学院科学技术研究项目(20110103)

摘　　要：利用反映模糊数整体和局部特征的三个重要指标:模糊数的均值,截集的中点和扩展,本文提出一种新的模糊数排序方法。该方法将每个模糊数独立地映射到实数轴上,得到一个以数字大小为基准的自然顺序,不仅体现决策者对各排序指标的偏好,而且无需对模糊数进行两两比较,计算简便,易于理解,尤其是对三角和梯形模糊数而言,数值实验表明该方法在一定程度上克服了已有方法的缺陷。Taking advantage of three indices embodying the overall characteristics and the partial ones of fuzzy numbers： the mean values of fuzzy numbers, the middle points and spreads of α-cut sets, this paper proposes a new approach to rank fuzzy numbers. It maps each fuzzy number to the real number axis independently, and obtains a natural order with digital size as a benchmark. The proposed method not only reflects the preference of the decision-maker, but also can be understood without any difficulty. The ranking process is simple and efficient for the calculation because of deleting the necessity of pairwise comparison, especially in ranking triangular and trapezoidal fuzzy numbers. Numerical experiments indicates that this approach can overcome some pitfalls rooted in most existing ranking methods to some extent.

关 键 词：模糊数 排序方法 α-截集 均值 中点 扩展 

分 类 号：O174[理学—数学]