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.     

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.     

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.     

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.     

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。     

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。     

Fuzzy sets in urban design

Urban design review has traditionally been fraught with allegations of subjectivity. While reviewers strive to ensure projects that are in the best interests of the community, the mechanisms for and language of evaluation are often arbitrary and inconsistent. With any evaluation process, the more objective and standardized the assessment instruments are, the more assurance is afforded by the community. The proposed ‘urban design assessment model’ is one mechanism based on the mathematical concepts of fuzzy set theory that attempts to address this problem, while assuming a role as a tool to complement rather than supplant existing mechanisms of review. The paper is presented in four parts. The first part is the introduction to the paper. The second part briefly explains the term ‘urban design’ and the different approaches to urban design review. The third part describes the proposed urban design assessment model. This section also discusses the basic concept of the fuzzy set and explains the model through an example. In the fourth part, the conclusion of the paper, the strengths and weaknesses of the proposed model are examined     

A duality theory for decomposable systems in a category

The Arbib-Manes duality theory for decomposable systems in a category is generalized, making it possible to apply the theory to infinite-dimensional linear systems in reflexive Banach spaces.     

Distance and similarity measures for hesitant fuzzy sets

In this paper, we propose a variety of distance measures for hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant ordered weighted distance measures and hesitant ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Several numerical examples are provided to illustrate these distance and similarity measures.     

The cut sets,decomposition theorems and representation theorems on intuitionistic fuzzy sets and interval valued fuzzy sets

In this paper,the cut sets,decomposition theorems and representation theorems of intuitionistic fuzzy sets and interval valued fuzzy sets are researched indail.First,new definitions of four kinds of cut sets on intuitionistic fuzzy sets are introduced,which are generalizations of cut sets on Zadeh fuzzy sets and have the same properties as that of Zadeh fuzzy sets.Second,based on these new cut sets,the decomposition theorems and representation theorems on intuitionistic fuzzy sets are established.Each kind ...     

Fuzzy relations and fuzzy groups

Given a group S, we consider fuzzy relations on S, that is, maps from S × S into [0,1]. Of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on S × S. We prove that if σ is a fuzzy subset of S and μ_σ is the strongest fuzzy relation on S that is a fuzzy relation on σ, then μ_σ is a fuzzy subgroup if and only if σ is a fuzzy subgroup. A number of other results are obtained about the interrelationships between fuzzy relations on S (including the weakest fuzzy relation) and fuzzy subgroups on S × S.     

Completions of cut systems in Q-sets

Let $ Q$ be a complete residuated lattice. Let $\text {SetR}(Q)$ be the category of sets with similarity relations with values in $ Q$ (called $ Q$ -sets), which is an analogy of the category of classical sets with relations as morphisms. A cut in an $ Q$ -set $(A,\delta )$ is a system $(C_{\alpha })_{\alpha \in Q}$ , where $C_{\alpha }$ are subsets of $A\times Q$ . It is well known that in the category $\text {SetR}(Q)$ , there is a close relation between special cuts (called f-cuts) in an $ Q$ -set on one hand and fuzzy sets in the same $ Q$ -set, on the other hand. Moreover, there exists a completion procedure according to which any cut $(C_{\alpha })_{\alpha }$ can be extended onto an f-cut $(\overline{C_{\alpha }})_{\alpha }$ . In the paper, we prove that the completion procedure is, in some sense, the best possible. This will be expressed by the theorem which states that the category of f-cuts is a full reflective subcategory in the category of cuts.