关于二型模糊集合的一些基本问题

发布时间：2018-12-27 17:52

【摘要】：采用集合论的方法给出了单位模糊集合和二型模糊集合及其在一点的限制等定义,使得二型模糊集合更易于理解.通过定义嵌入单位模糊集合来描述一般二型模糊集合,并给出离散、半连通二型模糊集合的表达式.根据论域、主隶属度及隶属函数的特性将二型模糊集合分为四种类型:离散、半连通、连通及复合型,并根据连通的特点将连通二型模糊集合分为单连通及多连通两类.利用支集的闭包(Closure of support,CoS)划分法表述主隶属度及区间二型模糊集合.提出了CoS二、三次划分法分别来表述单、复连通二型模糊集合,并使每一个子区域的上下边界及次隶属函数在该子区域上的限制分别具有相同的解析表述式.最后,探讨了二型模糊集合在一点的限制、主隶属度、支集、嵌入单位模糊集合之间的关系.
[Abstract]:The definitions of unit fuzzy set and type 2 fuzzy set and their limitation at one point are given by means of set theory, which makes the type 2 fuzzy set easier to understand. The general type 2 fuzzy sets are described by defining embedded unit fuzzy sets, and the expressions of discrete, semi-connected type 2 fuzzy sets are given. According to the properties of the domain, the principal membership degree and membership function, the second type fuzzy sets are divided into four types: discrete, semi-connected, connected and composite, and the connected two-type fuzzy sets are divided into simple connected and multi-connected fuzzy sets according to the characteristics of connectivity. The main membership degree and interval type 2 fuzzy set are expressed by the closure (Closure of support,CoS partition method of the branch set. In this paper, the CoS quadratic and cubic partition methods are proposed to describe the simple and complex connected type 2 fuzzy sets, respectively, and the upper and lower boundary of each subregion and the limitation of the submembership function on the subdomain are respectively expressed with the same analytic expression. Finally, the relationship between the restriction of type 2 fuzzy set at one point, the principal membership degree, the branch set and the embedded unit fuzzy set is discussed.
【作者单位】：中国科学院自动化研究所复杂系统管理与控制国家重点实验室;国防科学技术大学军事计算实验与平行系统技术研究中心;长沙理工大学电气与信息工程学院;
【基金】：国家自然科学基金(61533019,71232006,61233001,61074093,61473048)资助~~
【分类号】：O159

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