Fuzzy sets and similarity relations for semantic web service matching

Semantic Web Services (SWS) were introduced to facilitate the publication, discovery, and execution of web services. A semantic matchmaker enhances the capability of UDDI service registries in the SWS architecture and it is able to recognize various degrees of matching for web services. On the basis of SWS and fuzzy-set theory, a fuzzy matching approach for semantic web services is proposed, to support a more automated and veracious service discovery process.     

Fuzzy logic models in a category of fuzzy relations

We investigate interpretations of formulas ψ in a first order fuzzy logic in models which are based on objects of a category SetR(Ω) which consists of Ω-sets, i.e. sets with similarity relations with values in a complete MV-algebra Ω and with morphisms defined as special fuzzy relations between Ω-sets. The interpretations are then morphisms in a category SetR(Ω) from some Ω-set to the object . We define homomorphisms between models in a category SetR(Ω) and we prove that if is a (special) homomorphism of models in a category SetR(Ω) then there is a relation between interpretations of a formula ψ in models . Supported by MSM6198898701, grant 201/07/0191 of GAČR and grant 1M0572.     

Isomorphisms and functors of fuzzy sets and cut systems

Any fuzzy set \(X\) in a classical set \(A\) with values in a complete (residuated) lattice \( Q\) can be identified with a system of \(\alpha \) -cuts \(X_{\alpha }\) , \(\alpha \in Q\) . Analogical results were proved for sets with similarity relations with values in \( Q\) (e.g. \( Q\) -sets), which are objects of two special categories \({\mathbf K}={Set}( Q)\) or \({SetR}( Q)\) of \( Q\) -sets, and for fuzzy sets defined as morphisms from an \( Q\) -set into a special \(Q\) -set \(( Q,\leftrightarrow )\) . These fuzzy sets can be defined equivalently as special cut systems \((C_{\alpha })_{\alpha }\) , called f-cuts. This equivalence then represents a natural isomorphism between covariant functor of fuzzy sets \(\mathcal{F}_{\mathbf K}\) and covariant functor of f-cuts \(\mathcal{C}_{\mathbf K}\) . In this paper, we prove that analogical natural isomorphism exists also between contravariant versions of these functors. We are also interested in relationships between sets of fuzzy sets and sets of f-cuts in an \(Q\) -set \((A,\delta )\) in the corresponding categories \({Set}( Q)\) and \({SetR}( Q)\) , which are endowed with binary operations extended either from binary operations in the lattice \(Q\) , or from binary operations defined in a set \(A\) by the generalized Zadeh’s extension principle. We prove that the resulting binary structures are (under some conditions) isomorphic.     

模糊相似关系下变精度模糊粗糙集

经典变精度模糊粗糙集模型是基于模糊等价关系建立的.在实际应用中,模糊等价关系很难直接构造,需要通过求模糊相似关系的传递闭包生成.对模糊关系的这种改造会丢失较多有价值的信息,而且还增大了模糊粗糙集应用的计算复杂度.基于模糊逻辑算子构造2个模糊集的相对错误包含度,构造性地提出基于模糊相似关系的变精度模糊粗糙集模型,研究了该模型的性质.该模型一方面具有变精度粗糙集的优点,对噪声数据具有很好的容错能力,另一方面是基于模糊相似关系建立的,其应用范围更为广泛.     

基于Vague集相似度量的模糊分类

在区间值模糊集理论和Vague集理论的基础上,提出了一种新的基于Vague集相似度量的模糊分类方法,对Fisher建立的Iris数据库进行了分类实验处理,分类结果的正确率超过95%。该方法计算简单有效,具有一定的实际应用价值。     

Fuzzy sets based knowledge systems and knowledge elicitation

Fuzzy sets are adequate forms of knowledge representation when the information is uncertain due to vagueness and imprecision. Knowledge structures using fuzzy sets are similar to those implemented in non-fuzzy systems. Classical knowledge elicitation methods can be used in combination with techniques to develop membership functions. The fuzzy set representation has several advantages, including flexibility in expressing uncertain knowledge during elicitation, representation of the knowledge and its uncertainty as a unique entity, easy interfacing with classical systems, and a more robust system in ill-defined domains. These advantages result in increased system reliability.     

Inclusion measures,similarity measures,and the fuzziness of fuzzy sets and their relations

The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures, similarity measures, and the fuzziness of fuzzy sets can be transformed by each other based on their axiomatic definitions, and propose some new formulas to calculate inclusion measures, similarity measures, and the fuzziness of fuzzy sets. These results can be applied in many fields, such as pattern recognition, image processing, fuzzy neural networks, fuzzy reasoning, and fuzzy control. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 639–653, 2006.     

The three-dimensional fuzzy sets and their cut sets

In this paper, a new kind of L-fuzzy set is introduced which is called the three-dimensional fuzzy set. We first put forward four kinds of cut sets on the three-dimensional fuzzy sets which are defined by the 4-valued fuzzy sets. Then, the definitions of 4-valued order nested sets and 4-valued inverse order nested sets are given. Based on them, the decomposition theorems and representation theorems are obtained. Furthermore, the left interval-valued intuitionistic fuzzy sets and the right interval-valued intuitionistic fuzzy sets are introduced. We show that the lattices constructed by these two special L-fuzzy sets are not equivalent to sublattices of lattice constructed by the interval-valued intuitionistic fuzzy sets. Finally, we show that the three-dimensional fuzzy set is equivalent to the left interval-valued intuitionistic fuzzy set or the right interval-valued intuitionistic fuzzy set.     

结合类别相关性和辨识集的特征选择方法

介绍了基于辨识集的属性约简算法,把该属性约简算法同类别相关性结合起来,提出了一个综合的特征选择方法.该综合方法使用类别相关性进行特征初选,并用所提属性约简算法消除冗余.实验结果表明此种特征选择方法能够获得较具代表性的特征子集.     

一种基于分类和相似度的报警聚合方法

提出一种报警聚合方法,将所有报警按攻击类别分为四类,不同报警属性根据其值的特点分为四类,在此基础上采取不同的属性相似度计算方法,设置不同的期望阈值,可通过外部接口在运行时动态调整阈值。属性相似度结果依据不同分类在最后结果中占据不同权重,聚合判决依赖于所有相似度的加权平均结果,聚合结果取决于具有最大相似度的超报警是否大于给定的阈值。实验结果表明,本算法能有效减少重复告警。     

Non-standard cut classification of fuzzy sets

Several important non-standard cut sets of lattice-valued fuzzy sets are investigated. These are strong cuts, “not less” and “neither less nor equal” cuts. In each case it is proved that collection of all cuts of any lattice-valued fuzzy set form a complete lattice under inclusion. Decomposition theorem (representation by cuts) is proved for “neither less nor equal” cuts. Necessary and sufficient conditions under which two lattice-valued fuzzy sets with the same domain have equal families of corresponding cut sets are given.     

二元截集下的Vague集的分解定理

为了揭示Vague集和经典集之间的联系,在Vague集二元截集的基础上,提出了两个新的Vague集的分解定理。Vague集的分解定理表明Vague集可以由它分解出的截集簇来表示,而这些截集簇都是普通集。最后实例说明了其有效性。     

Vague相似关系与Vague划分

通过对单位区间[0,1]的闭子区间集中的元素——Vague值的定义,引入二元Vague关系、关系运算、逆关系、关系的合成、λ-截关系等新的定义。从基于可能度的区间数序关系的概念以及Vague集投票模型的实际意义两个方面,引入闭子区间集中Vague值的偏序关系的定义,并利用偏序关系证明了Vague关系的一些主要性质。给出了满足sup-min传递性的Vague相似关系以及Vague划分的定义,建立了Vague相似关系与Vague划分一一对应性,进而以[0,1]上连续t模作为广义的“与”逻辑算子,引入Vague相似关系的特例——满足T-传递性的Vague T-相似关系与Vague T-划分新的定义。     

A property of structural numbers and cut sets

The classical theory of structural numbers and its relations with graphs are used in this work to determine a property concerning cut sets in graphs. This work has been supported partially by Comitato per la Matematica C. N. R., under research contract N. 75.01035.01.     

对模糊集、粗糙集和Vague集的比较研究

模糊集、粗糙集和Vague集三种理论都是对经典集合理论的扩展,使得集合论的应用扩展到了含糊的、不确定性的问题领域。介绍了三种集合的基本思想,重点分析三种理论的区别和内在联系,同时对三种理论的发展及应用作了一些探讨性研究。     

Vague集及其相似度量的新方法

相似度量是Vague集研究中的一个重要内容,对于知识表达、模式识别等研究具有重要意义。引入了Vague值（集）相似度量的基本准则,并对现有的一些Vague值（集）相似度量方法进行研究,发现目前Vague值（集）相似度量方法存在一些缺陷,因此提出了一种新的Vague值（集）的相似度量方法,并通过数据分析验证了新方法的有效性。     

Parameterizing cut sets in a graph by the number of their components

For a connected graph G=(V,E), a subset U⊆V is a disconnected cut if U disconnects G and the subgraph G[U] induced by U is disconnected as well. A cut U is a k-cut if G[U] contains exactly k(≥1) components. More specifically, a k-cut U is a (k,?)-cut if V?U induces a subgraph with exactly ?(≥2) components. The Disconnected Cut problem is to test whether a graph has a disconnected cut and is known to be NP-complete. The problems k-Cut and (k,?)-Cut are to test whether a graph has a k-cut or (k,?)-cut, respectively. By pinpointing a close relationship to graph contractibility problems we show that (k,?)-Cut is in P for k=1 and any fixed constant ?≥2, while it is NP-complete for any fixed pair k,?≥2. We then prove that k-Cut is in P for k=1 and NP-complete for any fixed k≥2. On the other hand, for every fixed integer g≥0, we present an FPT algorithm that solves (k,?)-Cut on graphs of Euler genus at most g when parameterized by k+?. By modifying this algorithm we can also show that k-Cut is in FPT for this graph class when parameterized by k. Finally, we show that Disconnected Cut is solvable in polynomial time for minor-closed classes of graphs excluding some apex graph.     

二元截集下Vague集的表现定理及扩展原理

在Fuzzy集和Vague集理论的基础上,根据二元截集下集合套的概念和Vague集的分解定理,得出新的Vague集的表现定理、扩展原理,并且讨论了相关的代数性质,清楚地表现了经典集与Vague集之间的联系。