模糊多属性决策的相似接近度解法

首先对模糊集合的3种接近度测度,即海明距离、模糊贴近度和灰色关联度进行讨论,在此基础上提出了相似接近度的概念,运用模糊满意度的概念建立了模糊多属性决策的数学模型,其次将相似接近度的概念应用于该模型,提出了该模型的一个新的解法;最后通过数值算例表明,该方法不但十分有效,而且物理意义和数学意义明确,模糊贴近度、灰色关联度和相对接近度解法都是该方法的特例．

On similar approach degree algorithm for fuzzy multiple attribute decision-making

Fuzzy multiple attribute decision-making (FMADM) is a problem of multiple criteria decision making (MCDM) whose decision space is discrete considering the fuzzy information. Firstly, three kinds of measures of approach degree between two fuzzy sets are discussed, and then, a new concept named similar approach degree is put forward. A mathematical model of FMADM is built by means of fuzzy satisfaction degree. The concept of similar approach degree is applied in model, and then, a new algorithm for solving the model is proposed which is applied in the selection of the optimal scheme of large-span spatial structures. It is shown by a numerical example that this method is not only very efficient, but also clear both in mathematical meanings and in physical meanings. In fact, the algorithms of fuzzy nearness degree, grey association degree and relative approach degree all are the specific ones of the methodology proposed herein.