Robustness of interval-valued fuzzy inference

Since interval-valued fuzzy set intuitively addresses not only vagueness (lack of sharp class boundaries) but also a feature of uncertainty (lack of information), interval-valued fuzzy reasoning plays a vital role in intelligent systems including fuzzy control, classification, expert systems, and so on. To utilize interval-valued fuzzy inference better, it is very important to study the fundamental properties of interval-valued fuzzy inference such as robustness. In this paper, we first discuss the robustness of interval-valued fuzzy connectives. And then investigate the robustness of interval-valued fuzzy reasoning in terms of the sensitivity of interval-valued fuzzy connectives and maximum perturbation of interval-valued fuzzy sets. These results reveal that the robustness of interval-valued fuzzy reasoning is directly linked to the selection of interval-valued fuzzy connectives.     

Fuzzy rough set theory for the interval-valued fuzzy information systems

The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory, i.e., the interval-valued fuzzy rough set model is presented based on the interval-valued fuzzy information systems which is defined in this paper by a binary interval-valued fuzzy relations RF⁽ⁱ⁾(U×U) on the universe U. Several properties of the rough set model are given, and the relationships of this model and the others rough set models are also examined. Furthermore, we also discuss the knowledge reduction of the classical Pawlak information systems and the interval-valued fuzzy information systems respectively. Finally, the knowledge reduction theorems of the interval-valued fuzzy information systems are built.     

基于包含度的直觉模糊粗糙集模型

将直觉模糊包含度引入粗糙集与直觉模糊集的融合建模。首先,介绍直觉模糊集在特殊格L上的定义;其次,将模糊包含度拓展到直觉模糊环境下,提出取值于特殊格L的直觉模糊包含度定义和计算公式;在此基础上,分别利用直觉模糊包含度的隶属度与非隶属度定义了上下近似算子,建立了直觉模糊相似关系下的直觉模糊粗糙集模型,并对近似算子的重要性质进行了证明。     

基于表现定理的粗糙模糊集的构造方法

基于模糊集的截集和表现定理,从新的角度建立了粗糙模糊集的近似算子,强近似算子和弱近似算子,并得到粗糙模糊集的两种新的描述形式。     

基于直觉模糊粗糙集的属性约简

针对Jensen下近似定义的局限性,提出一种新的等价类形式的近似算子表示,并将其推广到直觉模糊环境.在此基础上,将相对正域、相对约简、相对核等粗糙集的知识约简概念推广到直觉模糊环境,提出一种直觉模糊信息系统的启发式属性约筒算法.实例计算表明.该方法比Jensen的属性约简方法更为合理有效.     

Variable precision intuitionistic fuzzy rough set model and applications based on conflict distance

Due to the complexity and uncertainty of the physical world, as well as the limitation of human ability to comprehend, it is very difficult for any single method of uncertainty to effectively deal with the decision‐making problem that exists in real life. So, it is natural for us to think about incorporating the advantages of various theories of uncertainty to develop a more powerful hybrid method of soft decision‐making. In view of this recognition, the thought and method of intuitionistic fuzzy sets and variable precision rough sets are used to construct a novel intuitionistic fuzzy rough set model. With respect to the fact that the information system is intuitionistic fuzzy, the idea of measuring intuitionistic fuzzy similarity is used to define conflict distance. After that, this concept is combined with the variable precision rough sets so that a variable precision intuitionistic fuzzy rough set model is established, and its properties are investigated. After proposing an attribute reduction algorithm based on variable precision intuitionistic fuzzy rough sets, a case study is used to verify the feasibility and effectiveness of our novel model. The results show that our model indeed improves the classification ability of earlier models and possesses some ability to tolerate faults through adjusting the parameter λ and the confidence threshold β; it realizes the correct classification and extracts the decision rules.     

Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications

In this paper we propose an entropy measure for interval-valued intuitionistic fuzzy sets, which generalizes three entropy measures defined independently by Szmidt, Wang and Huang, for intuitionistic fuzzy sets. We also give an approach to construct similarity measures using entropy measures for interval-valued intuitionistic fuzzy sets. In particular, the proposed entropy measure for interval-valued intuitionistic fuzzy sets can yield a similarity measure. Several illustrative examples are given to demonstrate the practicality and effectiveness of the proposed formulas. We apply the similarity measure to solve problems on pattern recognitions, multi-criteria fuzzy decision making and medical diagnosis.     

单向S-区间值模糊粗糙集及应用

以Z.Pawlak粗集理论为基础,将动态区间值模糊近似概念引入区间值模糊粗糙集中。由此提出了单向S-区间值模糊粗糙集概念,给出了单向S-区间值模糊粗糙集的结构与性质。定义了单向S-区间值模糊粗糙集的粗相等、截集、粗糙度等概念,并对一些相关性质进行讨论和证明;给出了单向S-区间值模糊粗糙集的应用及存在价值。     

一种基于粗集理论的动态近似规则挖掘推理方法

提出一种基于粗集理论的,把属性的重要性和属性值的出现频率综合起来进行规则推理的方法.分析了“激活一个,否则离开”原则的优缺点,指出在近似推理中,大前提中的规则数量应该可变.给出一种根据推理过程中规则的出现频率决定其是否保留,从而实现规则数量的动态变化的方法,证明了动态变化过程中规则的数量不会无限增加.实例表明此法是比较有效的.     

模糊粗糙集的鱼病规则获取方法

针对鱼病诊断中存在随机性、诊断信息的模糊性和信息获取的不完备性等不确定因素。首先给出模糊的鱼病诊断过程,由于该方法存在模糊诊断矩阵较难获取的缺点。利用粗糙集理论无需先验知识的优点,将粗糙集理论和模糊集结合用于鱼病的诊断中。鱼病的症状模糊集形成条件属性,疾病模糊集形成决策属性构成模糊信息表,给出了模糊信息表属性约简和鱼病诊断规则获取的算法步骤,最后以实例演示了鱼病诊断的规则获取过程。论文为鱼病的诊断提供了一种全新的方法。     

基于区间直觉模糊集的多准则决策方法

研究基于区间直觉模糊集的多准则决策方法.首先定义了区间直觉模糊点算子,并讨论了其性质;然后对区间直觉模糊集定义了一系列得分函数,并给出两种基于区间直觉模糊集的多准则决策方法.将该方法应用于区间直觉模糊集多准则决策问题,所得结果推广了有关直觉模糊集的相关结果.     

变精度粗糙模糊集模型研究

介绍了Ziarko’s变精度粗糙集模型和粗糙模糊集模型,找出了它们的不足。基于支集相对错误分类率及误差参数β（0≤β<0.5）,提出了变精度粗糙模糊集模型,讨论了模型中β上、下近似算子的性质;分析了该模型与Ziarko’s变精度粗糙集模型和粗糙模糊集模型的关系;最后给出了该模型中近似约简的定义和方法,并通过实例分析说明了约简算法的有效性。     

A method based on distance measure for interval-valued intuitionistic fuzzy group decision making

In this paper we introduce some relations and operations of interval-valued intuitionistic fuzzy numbers and define some types of matrices, including interval-valued intuitionistic fuzzy matrix, interval-valued intuitionistic fuzzy similarity matrix and interval-valued intuitionistic fuzzy equivalence matrix. We study their properties, develop a method based on distance measure for group decision making with interval-valued intuitionistic fuzzy matrices and, finally, provide an illustrative example.     

基于模糊粗糙集的TOPSIS供应商评估方法

由于供应商选择是一个多目标评价问题, 不确定的因素很多, 如果仅靠经验判断则无法避免结果的主观性, 针对这一问题采用了定性和定量相结合的方法, 利用模糊粗糙集求得指标的客观权重, 利用专家评分法来定义指标的主观权重, 再综合主客观权重, 最后将综合权重用于TOPSIS进行评估, 并用实例证明了这种方法的有效性和可行性。     

Positive approximation and converse approximation in interval-valued fuzzy rough sets

Methods of fuzzy rule extraction based on rough set theory are rarely reported in incomplete interval-valued fuzzy information systems. Thus, this paper deals with such systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. The data completeness of missing attribute values is first presented. Positive and converse approximations in interval-valued fuzzy rough sets are then defined, and their important properties are discussed. Two algorithms based on positive and converse approximations, namely, mine rules based on the positive approximation (MRBPA) and mine rules based on the converse approximation (MRBCA), are proposed for rule extraction. The two algorithms are evaluated by several data sets from the UC Irvine Machine Learning Repository. The experimental results show that MRBPA and MRBCA achieve better classification performances than the method based on attribute reduction.     

结合模糊集理论的粗糙集属性约简算法*

结合模糊关系的理论,对粗糙集理论的属性约简算法进行研究,提出了一个新的属性约简算法,并给出了一个应用实例.     

基于FCM的相似关系粗糙集属性约简方法

对具有连续属性值的信息系统的属性约简是粗糙集理论的研究热点之一。区别于传统通过连续属性离散化方法定义的等价关系,提出利用自适应的模糊C均值聚类的初步划分能力定义一种相似关系以及其自适应形式。基于该相似关系定义的粗糙集模型较好地排除噪声数据。提出正域与非正域定义以及从中导出的一种重要度以指导属性约简。与现有方法的比较实验表明该方法在属性约简上具有有效性和稳定性以及约简结果的合理性。     

Intuitionistic fuzzy rough set model based on conflict distance and applications

Due to the complexity and uncertainty of the objective world, as well as the limitation of human ability to understand, it is difficult for one to employ only a single type of uncertainty method to deal with the real-life problem of decision-making, especially problems involving conflicts. On the other hand, by incorporating the advantages of various theories of uncertainty, one is expected to develop a more powerful hybrid method for soft decision making and to solve such problems more effectively. In view of this, in this paper the thought and method of intuitionistic fuzzy set and rough set are used to construct a novel intuitionistic fuzzy rough set model. Corresponding to the fact that the decision-making information system of rough sets is of intuitionistic fuzzy information system, our method defines the conflict distance by using the idea of measuring intuitionistic fuzzy similarity so that it is introduced into the models of rough sets, leading to the development of our intuitionistic fuzzy rough set model. After that, we investigate the properties of the model, introduce a novel tool for conflict analysis based on our hybrid model, and employ this new tool to describe and resolve a real-life conflict problem.     

覆盖粗糙直觉Fuzzy集模型的一点注记

通过对一类覆盖粗糙直觉模糊集模型中粗糙度定义的分析,对其所存在疏漏进行了改进;再将粗糙熵的概念引入到该模型,研究直觉模糊集的不确定度量;通过例子说明该度量的有效性。     

基于粗糙集和模糊聚类的政务本体学习模型

根据政务信息资源的特点,提出了一种新的政务本体学习模型。首先通过命名实体获取领域概念,然后利用粗糙集和模糊聚类理论对模式匹配算法进行改进,进而采用改进的模式匹配算法获取领域概念之间的显式和隐式关系。大量的实践证明：利用该模型能够从庞大的政务信息资源中有效地进行政务本体学习,克服了传统模式匹配算法不能很好地获取概念之间隐式关系的问题。