不同知识粒度下粗糙集的不确定性研究

粗糙集的不确定性度量方法,目前主要包括粗糙集的粗糙度、粗糙熵、模糊度和模糊熵.在不同知识粒度下,从属性的角度,给出了分层递阶的知识空间链,发现在分层递阶的知识粒度下部分文献中定义的粗糙集的粗糙熵和模糊度随知识粒度的变化规律不一定符合人们的认识规律.从信息熵的角度提出了一种粗糙集不确定性的模糊度度量方法,证明了这种模糊度随知识粒度的减小而单调递减,弥补了现有粗糙熵和模糊度度量粗糙集不确定性的不足.最后,分析了在不同知识粒度下粗糙度和模糊度的变化关系.     

基于知识粒度的粗糙集的不确定性度量

粗糙集的不确定性与其所在近似空间知识粒度的大小密切相关.提出了近似空间中集合的相对知识粒度的概念.基于相对知识粒度的粗糙集的粗糙性度量既刻画了近似空间对粗糙集不确定性的影响,又去除了负域的干扰.从边界熵的角度提出了一种粗糙集的模糊性度量.随着近似空间知识粒的细分,粗糙集的粗糙度与模糊度均单调递减.     

粗糙集不确定性度量的矩阵运算

粗糙集的不确定性度量是粗糙集理论的重要研究内容之一。结合模糊理论和粒计算理论改进了粗糙集的不确定性度量方法。通过集合的相对知识粒度及边界熵给出了粗糙集的粗糙性度量函数与模糊性度量函数,随着近似空间知识粒的细分,粗糙集的粗糙度与模糊度均满足单调递减的性质。利用矩阵理论提出了易于实现的粗糙性度量与模糊性度量的矩阵算法。     

改进的直觉模糊粗糙集相似性度量方法

针对现有的直觉模糊粗糙集相似性度量的问题,提出了一种改进的基于海明距离的直觉模糊粗糙集相似性度量方法。该方法考虑了犹豫度并引入加权参数,解决了相似性度量不精确的问题。首先给出了直觉模糊粗糙值间的相似性度量定义,并揭示其若干重要性质。在此基础上,提出了直觉模糊粗糙集间的相似性度量方法,并证明其具有同样性质。最后通过数值算例分析说明了该方法更合理、更有效。     

层次粒结构下粗糙模糊集的不确定性度量

众所周知,经典粗糙集的不确定性来自于边界域,但是对于粗糙模糊集来说,其正域和负域中的元素存在不确定性,从而导致粗糙模糊集的不确定性不仅来自于边界域,还来自于正域和负域。另外,在粗糙模糊集中,一个模糊概念可以通过层次粒结构中不同的粗糙近似空间进行刻画,随着粒度的变化,模糊概念的不确定性的变化规律如何？对此,文中提出一种基于模糊度的不确定性度量公式,并基于均值模糊集分析了粗糙模糊集模型,得出粗糙模糊集不确定性度量的模型同样适合于度量概率粗糙集的不确定性的结论。其次,采用基于模糊度的不确定性度量方法,揭示了分层递阶的多粒度空间下粗糙模糊集不确定性的变化规律。然后,分析了3个域(正域、边界域和负域)的不确定性,并揭示了它们在分层递阶的多粒度空间下的变化规律。最后,通过实验验证了所提不确定性度量理论的有效性。     

基于信息粒化的区间值信息系统不确定性度量方法

目前区间值信息系统的不确定性度量方法大多基于粗糙集的粗糙度度量.实例分析表明该度量方法不满足严格单调性,为了解决这一缺陷,将粒计算方法引入区间值信息系统中,提出一种区间值信息系统的信息粒化模型.引入区间值信息系统的知识粒度和粗糙熵两种度量方法,理论分析出它们具有的严格单调性,在区间值信息系统的不确定性度量方面具有更好的优越性.实验验证了知识粒度和粗糙熵均比传统的粗糙度具有更好的不确定性度量效果.     

模糊粗糙集的相似度量和相似性方向

粗糙集理论是一种新的处理模糊和不确定性知识的软计算工具,在人工智能及认知科学等众多领域已经得到了广泛的应用。相似度量的研究是模糊集理论与粗糙集理论的热点问题之一。文章提出了一种更精确、更合理的相似度量方法,讨论了它的一些性质。然后,在此基础上提出了模糊粗糙集的相似性方向的概念,用于比较两个相似的模糊粗糙集所包含信息的精确性大小,并给出了一个关于相似性方向的判别函数。这在近似推理、模式识别和决策分析等领域有着广泛的应用。最后,通过一个实例,分析说明了这种相似度量方法和相似性方向的判别方法是更合理更有效的。     

K粒度模糊粗糙集模型的不确定性研究

粗糙集扩展模型的研究是粗糙集理论研究的一个重要问题,在引入了K粒度粗糙关系基础上定义了K粒度粗糙集模型并给出了K粒度分割概念,文章从信息熵的角度给出K粒度粗糙集模型的粗糙熵的不确定度量方法,讨论了该模型随知识分类粒度变化与粗糙熵之间的关系,证明了知识分类粒度呈细分时粗糙熵具有单调递增性,并且以实例验证了此模型理论的有效性与正确性,该模型使得粗糙集处理数据的范围扩展到了实域.在此基础上定义了K粒度模糊粗糙集模型,并研究了其结构及性质,最后给出了K粒度模糊粗糙集模型依参数0<β≤α≤1的扩展模型,并研究了模型的性质与粗糙度之间的关系.     

粗糙Vague集（值）相似性度量的一种新方法

对粗糙集和Vague集的概念、知识表示方法进行了讨论,把粗糙集和Vague集进行了融合,描述了粗糙Vague集概念,给出粗糙Vague值的相关概念及其相似性度量的一种新方法,研究了粗糙Vague集的相关性质及其相似性度量的方法。     

基于海明距离的直觉模糊粗糙集相似度量方法

针对直觉模糊粗糙集的相似度量问题,提出了一种基于海明距离的直觉模糊粗糙集相似度量方法。首先给出了两个直觉模糊粗糙值问的相似度量方法,并揭示了它的若干重要性质。然后,在此基础上,又提出了一种基于海明距离的直觉模糊粗糙集相似度量方法,并证明它也具有同样的性质。最后用数值算例验证了这种方法的有效性。     

A roughness measure of fuzzy sets from the perspective of distance

Covering generalized rough set theory is an important extension of classical rough set theory. To characterize a fuzzy set in a given covering approximation space, a pair of fuzzy sets, called covering rough fuzzy lower and upper approximations, were introduced, but they do not describe well how much uncertainty is induced by the granularity of knowledge. In this paper, we first discuss the relationship between uncertainty and granularity of knowledge. Then we examine several commonly used distance measures, and indicate that some of them exhibit some limitations. Next we propose a roughness measure based on Minkowski distance, and examine some important properties of this measure. Finally, an illustrative example is provided to demonstrate the application of the roughness measure to incomplete information systems with fuzzy decision.     

积模糊粗集模型及其模糊知识粒的表示和分解

为处理人工智能中不精确和不确定的数据和知识,Pawlak提出了粗集理论。之后粗集理论被推广,其方法主要有二:一是减弱对等价关系的依赖;二是把研究问题的论域从一个拓展到多个。结合这两种思想,研究基于两个模糊近似空间的积模糊粗集模型及其模糊粗糙集的表示和分解。根据这种思想,可以从论域分解的角度探索降低高维模糊粗糙集计算的复杂度问题。先对模糊近似空间的分层递阶结构———λ-截近似空间进行研究,得到不同层次知识粒的相互关系;然后定义模糊等价关系的积,并研究其性质及算法;最后构建基于积模糊等价关系的积模糊粗集模型,并讨论了该模型中模糊粗糙集的表示及分解问题,分别从λ-截近似空间和一维模糊近似空间的角度去处理,给出了可分解集的上(下)近似的一个刻画,及模糊可分解集的上(下)近似的λ-截集分解算法。     

Interpretable fuzzy partitioning of classified data with variable granularity

Fuzzy rule-based systems are effective tools for acquiring knowledge from data and represent it in a linguistically interpretable form. To achieve interpretability, input features are granulated in fuzzy partitions. A critical design decision is the selection of the granularity level for each input feature. This paper presents an approach, called DC^* (Double Clustering with A^*), for automatically designing interpretable fuzzy partitions with optimal granularity. DC^* is specific for classification problems and is mainly based on a two-stage process: the first stage identifies clusters of multidimensional samples in order to derive class-labeled prototypes; in the second stage the one-dimensional projections of such prototypes are further clustered along each dimension simultaneously, thus minimizing the number of clusters for each feature. Moreover, the resulting one-dimensional clusters provide information to define fuzzy partitions that satisfy a number of interpretability constraints and exhibit variable granularity levels. The fuzzy sets in each partition can be labeled by meaningful linguistic terms and used to represent knowledge in a natural language form. Experimental results on both synthetic and real data show that the derived fuzzy partitions can be exploited to define very compact fuzzy rule-based systems that exhibit high linguistic interpretability and good classification accuracy.     

Knowledge base to fuzzy information granule: A review from the interpretability-accuracy perspective

Fuzzy information granules indicate sufficiently interpretable fuzzy sets for achieving a high level of human cognitive abstraction. Furthermore, granularity, complexity, and accuracy are associated with fuzzy information granules. Measuring granularity is a promising means of verifying the effectiveness of the fuzzy granular model. Higher granularity indicates fine partitions, whereas coarser partitions suggest lower granularity. Therefore, accuracy is directly proportional to the granularity, such that, the higher the granularity, the more accurate and more complex the model is. Consequently, the granularity-simplicity tradeoff is also a significant criterion in considering the interpretability-accuracy tradeoff.This paper thoroughly reviews diverse ideas to understand the fuzzy information granule and addresses a sensible compromise between interpretability-accuracy and granularity-simplicity. Those requirements contradict each other, thus certain conceptual and mathematical considerations are necessary in designing a granular framework. Moreover, a double axis taxonomy is introduced in this paper: “complexity-based granularity versus semantic-based granularity” (which considers granularity measures) and “granular partition level versus granular rule base level” (regarding knowledge base stages). However, several constraints should be considered in designing a granular framework such as the granularity-accuracy dilemma, the overfitting/underfitting situation, the granular rule base level conflict, the interpretability constraint threshold, the stability-plasticity dilemma, and the parameter optimization. This paper primarily aims to present a conceptual framework to better understand existing methods, as well as how these methods can inspire future research.     

粒度聚类算法研究

信息粒度是对信息和知识细化的不同层次的度量。基于信息粒度的聚类分析方法,凭借能够灵活选择粒度结构,消除聚类结果和先验知识之间的不协调性,有效完成聚类任务等优点,成为国内外学者的研究热点之一。从粗糙集、模糊集、商空间3个理论角度与传统聚类算法相结合,阐述并分析了把粒度的思想引入到聚类中的有效算法及其优缺点,并对这样结合后处理高维复杂数据的可行性及有效性做了分析与展望。     

Fuzzy moves using normal fuzzy reasoning with fuzzy knowledge discovery

By merging the theory of moves (TOM) and the fuzzy sets theory, we have developed the theory of fuzzy moves (TFM) to make better fuzzy moves for fuzzy games. Since the data granularity of conventionally used fuzzy sets is too low to contain more heuristic information and mined knowledge, we take primary fuzzy sets with higher data granularity as fundamental elements for fuzzy reasoning so as to make more reasonable moves. The simulation results indicate that (1) TFM with normal fuzzy reasoning can make better and more reasonable moves than TOM with precise reasoning since different global strategies are taken into account by TFM and (2) the novel fuzzy reasoning methodology is more reasonable and more useful to make fuzzy moves than the conventional one. ©1999 John Wiley & Sons, Inc.     

关于模糊集的粗糙度

模糊集粗糙度的研究对于粗糙集和模糊集的理论和应用都有着重要作用。最近，Huynh等改进了由Baner—jee等给出的模糊集的粗糙度，提出了一种新的关于模糊集粗糙度的度量方法。本文对Huynh和Banerjee提出的粗糙度量进行了分析，指出了其中的不足，提出了一种新的改进方法。对Huynh度量方法存在缺陷的分析以及对新提出的改进方法性质的研究证明了新改进方法的合理性。     

基于包含度的变精度模糊粗糙集

利用模糊集的一个强包含度,在弱模糊划分的基础上建立了基于该包含度的变精度模糊粗糙集模型,对其重要性质进行了深入研究,并给出了对应形式粗糙度的计算方法,进一步利用海明距离和欧几里得距离定义了该模型下模糊粗糙集的两个粗糙性度量。给出的变精度模糊粗糙集模型能够使模糊粗糙集的运算按照模糊集的运算实现,为变精度模糊粗糙集理论的研究和应用莫定了一定的理论基础。