正态模糊集合——Fuzzy集理论的新拓展

Normal Distribution Fuzzy Sets——A New Extension of Fuzzy Sets

直觉模糊集(intuitionistic fuzzy sets)、区间值模糊集(interval-valued fuzzy sets)以及Vague集对普通fuzzy集的扩展是给出了隶属度的上下限,把隶属度从[0,1]区间中的一个单值推广到了[0,1]的子区间。但是该子区间犹如一个黑洞,隶属度在其内部的分布情况我们无从知晓,即这个子区间中的每一个值是等可能地作为元素的隶属度还是区间中的某些值较另外的值有更大的可能性呢?为了清晰的刻画出元素的隶属度在[0,1]区间中的分布情况,本文通过对投票模型的分析及正态分布理论,提出了一种新的模糊集合———正态模糊集合,同时对正态模糊集合的交、并、补等基本运算性质进行了讨论,文章最后对正态模糊集与fuzzy集、直觉模糊集的相互关系也作出了详细阐述。正态模糊集合是模糊集合理论的进一步推广,为我们处理模糊信息提供了一种全新的思想方法。

Comparing with the theory of fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets and vague sets extend the membership degree from a single value in [0,1] to a subinterval in [0,1] , but a more detailed information is that whether all the values in the subinterval have the same probability or some values have bigger probability than the others as a membership degree, we can not obtain. In this paper, according to the investigation of vote model we present a method for expressing intuitionistic fuzzy sets by a series of normal distribution functions, then the theory of normal distribution fuzzy sets is established. This theory can well solve the problem exist in the existing generalized fuzzy theories. The notion of inclusion, union, intersection, and complement are extended to such set, and various properties of normal distribution fuzzy sets are discussed. Normal distribution fuzzy sets are the extension of intuitionistic fuzzy sets, the relationships among fuzzy sets, intuitionistic fuzzy sets and normal distribution fuzzy sets are specified.