基于模糊语义量化函数的赋权方法及应用

由于客观事物具有的复杂性和不确定性,决策问题往往不能获得确切的权重信息,只能得到模糊语言形式的权重。为研究模糊语言形式的权重,首先定义了一种更广泛的四段折线型模糊语义量化函数,并给出了该函数的诸多基本性质,如单调性、非负有界性和归一性等,同时证明该函数在特殊情况下可退化为传统的三折线模糊语义量化函数。接着,根据定义的四段折线型模糊语义量化函数建立了一种新的权重确定方法。利用此方法确定的权重,便于计算其orness值,该值可用于度量决策者的乐观程度。最后,利用该赋权方法,对有序加权平均(OWA)算子中的权重进行赋值,并将其应用到一类权重为模糊语言形式的多属性决策问题中。所得结果表明了此方法的有效性与直观性。

A new weight determination method based on quantifiers and its application

Because of the complexity and uncertainty of objective reality, multi-attribute decision-making problems often cannot obtain exact weight information. The weight information is always given in fuzzy language form. In order to study such weight, this paper first defined a more extensive four segment broken line quantifier, and gave many basic properties of the quantifier, such as monotony, nonnegative boundedness and normalization. Meanwhile, it was also verified that the method proposed in this paper can degenerate into the traditional three segment broken line quantifier. Then, according to the four segment broken quantifier, a new weight determination method was established. The weight determined by this method was easy to calculate its "orness" value, which can be used to measure the degree of optimism of decision-makers. Finally, by this method, the weight of ordered weighted averaging operator was obtained, and then the ordered weighted averaging operator was applied to a multi-attribute decision making problem in which the weight was given by fuzzy language . The results show that the method proposed is effective and intuitive.