粗糙模糊集的模糊性度量

研究粗糙模糊集的模糊性度量，提出了一种新的熵与条件熵的概念，并验证了这种熵与Shannon熵类似的性质。利用这种熵定义了粗糙模糊集的一种不确定性度量，证明了粗糙模糊集的模糊性度量FR（A）等于0的充分必要条件是A是经典集合且是可定义的。     

模糊粗糙集代数

一个粗糙集代数是由一个集合代数加上一对近似算子构成的。本文用公理化方法定义了模糊环境下的近似算子和粗糙集代数系统。证明了若系统(Φ(U),∩,∪,-,L,H)是一个模糊粗糙集(粗糙模糊集)代数,则其导出的系统(Φ(U),∩,∪,-,LL,HH)也是模糊粗糙集(粗糙模糊集)代数,同时讨论了特殊类型的模糊粗糙集代数和粗糙模糊集代数与其导出的系统之间的关系。     

基于粗糙模糊集的聚类决策及应用

对基于粗糙模糊集的聚类问题进行了研究.首先,定义了粗糙模糊值与粗糙模糊集的相似度,给出了粗糙模糊集相似度的一般表达式;然后利用该公式构建了模糊相似矩阵,进而给出了粗糙模糊集的一种聚类方法;最后以实际算例说明了这种思想.     

覆盖粗糙模糊集的不确定性度量

在覆盖粗糙模糊集模型下,将粗糙集理论中的粗糙度和粗糙熵的概念引入到此模型中,用来度量模糊集的不确定的程度,并讨论了这些度量的一些性质.     

模糊粗糙近似算子公理集的独立性

用双论域上的模糊关系定义了广义模糊粗糙近似算子,并讨论了近似算子的性质。用公理刻画了模糊集合值算子,各种公理化的近似算子可以保证找到相应的二元模糊关系,使得由模糊关系通过构造性方法定义的模糊粗糙近似算子恰好就是用公理定义的近似算子。讨论了刻画各种特殊近似算子的公理集的独立性,从而给出各种特殊模糊关系所对应的模糊粗糙近似算子的最小公理集。     

基于模糊化邻域系的粗糙近似算子(Ⅰ)

模糊化邻域系源自模糊化拓扑空间.以模糊化邻域系为工具,定义了一对粗糙近似算子,研究了其基本性质.证明了这对算子涵盖一些常见粗糙近似算子作为其特殊情形,从而扩大了粗糙集理论的研究范围.此外,还研究了由串行的、反身的、一元的和传递的模糊化邻域系生成的粗糙近似算子.     

λ-模糊粗传递模型及其特性

根据实际中的三种信息传递情况,本文利用粗糙模糊集、模糊子集、截集等理论讨论了λ-模糊粗传递模型的特性,得到了λ-模糊粗传递模型与模糊粗传递模型的关系,给出了两种分解定理.以此为基础,分析了λ-模糊粗传递模型中信息的变化情况,给出了信息精确传递的条件,进一步得出了提高信息传递精确性的方法.λ-模糊粗传递是粗糙模糊集的一种新的应用.     

模糊粗糙集的表示及应用

一个模糊粗糙集是一对模糊集,它可以用一簇经典粗糙集表示出来.本文研究了模糊粗糙集的表示问题,利用模糊集的分解定理证明了一个模糊粗糙集可以用一簇粗糙模糊集表示出来,利用这个结果可以证明模糊粗糙集的一些重要性质.     

粗糙模糊集与模糊粗糙集的截集性质

研究粗糙模糊集、模糊粗糙集、广义粗糙模糊集和广义模糊粗糙集的截集性质,并且还研究了基于逻辑算子的广义模糊粗糙集的基本性质。     

区间值模糊集上的上(下)近似

定义区间值模糊粗糙集的上下近似,并且利用区间值模糊集的截集定义了区间值模糊粗糙度量。并且讨论了它们的性质。     

粗糙直觉模糊集的近似表示

在粗糙直觉模糊集的基础上,从新的角度提出了不确定目标概念的近似表示和处理的方法(通过近似模糊集和近似精确集刻画).首先将已有的直觉模糊集相似概念和均值直觉模糊集概念引入到该模型,定义了Pawlak近似空间U/R下的阶梯直觉模糊集、0.5-精确集的概念,然后得到了均值直觉模糊集(0.5-精确集)是所有直觉模糊集中与目标直觉模糊集最接近的直觉模糊集(近似精确集),接着分析了均值直觉模糊集、0.5-精确集分别与目标直觉模糊集的相似度随着知识粒度变化的变化规律.     

模糊粗糙集及粗糙模糊集的贴近度及其应用

本文研究了模糊粗糙集（FR集）及粗糙模糊集（RF集）的贴近度，是权衡两个FR集，两个RF集彼此糙近程度的一种标尺，进而研究了FR集，RF集的内积，外积，引进了FR集，RF集的格贴近度，并在此基础上提出一种新的属性约简的方法。     

On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse

This paper proposes a general study of (I,T)-interval-valued fuzzy rough sets on two universes of discourse integrating the rough set theory with the interval-valued fuzzy set theory by constructive and axiomatic approaches. Some primary properties of interval-valued fuzzy logical operators and the construction approaches of interval-valued fuzzy T-similarity relations are first introduced. Determined by an interval-valued fuzzy triangular norm and an interval-valued fuzzy implicator, a pair of lower and upper generalized interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy relation on two universes of discourse is then defined. Properties of I-lower and T-upper interval-valued fuzzy rough approximation operators are examined based on the properties of interval-valued fuzzy logical operators discussed above. Connections between interval-valued fuzzy relations and interval-valued fuzzy rough approximation operators are also established. Finally, an operator-oriented characterization of interval-valued fuzzy rough sets is proposed, that is, interval-valued fuzzy rough approximation operators are characterized by axioms. Different axiom sets of I-lower and T-upper interval-valued fuzzy set-theoretic operators guarantee the existence of different types of interval-valued fuzzy relations which produce the same operators.     

截集形式的模糊粗糙集及其性质

用模糊集的截集构造了模糊集的粗糙集,给出了模糊粗糙集的更加严格的数学定义,证明了与文[1]中的等价性,并用新的定义给出模糊粗糙集的相应性质.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

粗糙Vague集及其相似度量

对粗糙V ague集的基本操作和性质进行了研究。另外,对粗糙V ague集的相似度量问题进行研究,首先构造一种粗糙V ague值的相似度函数并给出其基本性质,然后给出一种粗糙V ague集的相似度函数以及一种粗糙V ague集的加权相似度函数。     

Similarity,inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral

Similarity measures of type-2 fuzzy sets are used to indicate the similarity degree between type-2 fuzzy sets. Inclusion measures for type-2 fuzzy sets are the degrees to which a type-2 fuzzy set is a subset of another type-2 fuzzy set. The entropy of type-2 fuzzy sets is the measure of fuzziness between type-2 fuzzy sets. Although several similarity, inclusion and entropy measures for type-2 fuzzy sets have been proposed in the literatures, no one has considered the use of the Sugeno integral to define those for type-2 fuzzy sets. In this paper, new similarity, inclusion and entropy measure formulas between type-2 fuzzy sets based on the Sugeno integral are proposed. Several examples are used to present the calculation and to compare these proposed measures with several existing methods for type-2 fuzzy sets. Numerical results show that the proposed measures are more reasonable than existing measures. On the other hand, measuring the similarity between type-2 fuzzy sets is important in clustering for type-2 fuzzy data. We finally use the proposed similarity measure with a robust clustering method for clustering the patterns of type-2 fuzzy sets.     

A new method for similarity measures for pattern recognition

This paper points out three questionable areas in the realm of similarity measures and then provides a new method that will rectify the problem. The purpose of this paper is fourfold. First, we will propose a scenario where the three similarity measures proposed by Hung and Yang (2004) [1] are helpless in aiding a decision maker in deciding pattern recognition problem. Second, we will present our method for solving the dilemma. Third, we will show that our proposed similarity measures satisfy the axioms for well defined similarity measures. Fourth, we will prove that our method could solve pattern recognition problems. Our findings will help researchers handle similarity problems under intuitionistic fuzzy sets environment.     

基于Type-2模糊贴近度在生态上的应用

分析比较了Type-1模糊贴近度与Type-2贴近度的特点,并将Type-2模糊贴近度的概念和相应运算应用到生态系统中,给出了物种动态的生态位模型,计算了物种实际生态位与理想生态位的重叠,根据重叠的精确值和区间值分别研究了物种进化的动态行为和进化程度.