Vague集之间的相似度量及其在机械设计方案决策中的应用

Similarity Measures between Vague Sets and Their Applications to the Decision Making in Machine Design Schemes

针对模糊集的推广形式——Vague集,描述了元素相对Vague集隶属情况的三维表示,当考虑不确定度(踌躇度)对肯定与否定隶属程度的影响时,可把不确定度细分成三部分倾向:肯定、否定和不确定,然后将元素在Vague集中被重新构成三部分:肯定隶属度、否定隶属度和不确定度,进而提出一种改进的Vague集之间相似度量方法,并应用于机械设计方案决策中.在机械设计方案决策中,Vague集之间的相似度量是评价设计方案接近期望方案(理想方案)的度量,相似度量值越大,设计方案接近期望方案越好.最后通过实例阐明Vague集之间的相似度量在机械设计方案决策中的有效性,且这种决策方法比现有决策方法更加合理、实用.

3 - D presentation of membership situation of an element to a vague setwas described, aiming at the extended form of fuzzy set--vague set. While the influence of uncertain degree （hesitancy degree） upon certain membership degree and negative membership degree may be considered here, the uncertain degree may be subdivided into three tendencies： certainty, negation and uncertainty. Then, the element in a vague set was composed over again of the three parts： certain membership degree, negative membership degree and uneertain degree. Further, an improved method of similarity measures between vague sets was proposed and was applied to the decision - making in machine design schemes. In the decision - making in machine design schemes, similarity degree between vague sets is a mea- surement to evaluate how the design scheme is close to the expected one （ideal one）. The bigger the value similarity measures is, the better the close degree between the design scheme and the expected scheme is. Finally, the validity of similarity measure of vague sets in decision - making in machine design schemes is illustrated, and this decision - making method is more reasonable and more practical than the ones current in use.