Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction

As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.

On Multi-Granulation Rough Sets with Its Applications

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

Intuitionistic Fuzzy Rough Sets Based on Two Intuitionistic Fuzzy Implicators

This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.

Interval-Valued Intuitionistic Fuzzy-Rough Sets

This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.

Domain-Oriented Data-Driven Data Mining Based on Rough Sets

Data mining (also known as Knowledge Discovery in Databases - KDD) is defined as the nontrivial extraction of implicit, previously unknown, and potentially useful information from data. The aims and objectives of data mining are to discover knowledge of interest to user needs.Data mining is really a useful tool in many domains such as marketing, decision making, etc. However, some basic issues of data mining are ignored. What is data mining? What is the product of a data mining process? What are we doing in a data mining process? Is there any rule we should obey in a data mining process? In order to discover patterns and knowledge really interesting and actionable to the real world Zhang et al proposed a domain-driven human-machine-cooperated data mining process.Zhao and Yao proposed an interactive user-driven classification method using the granule network. In our work, we find that data mining is a kind of knowledge transforming process to transform knowledge from data format into symbol format. Thus, no new knowledge could be generated (born) in a data mining process. In a data mining process, knowledge is just transformed from data format, which is not understandable for human, into symbol format,which is understandable for human and easy to be used.It is similar to the process of translating a book from Chinese into English.In this translating process,the knowledge itself in the book should remain unchanged. What will be changed is the format of the knowledge only. That is, the knowledge in the English book should be kept the same as the knowledge in the Chinese one.Otherwise, there must be some mistakes in the translating proces, that is, we are transforming knowledge from one format into another format while not producing new knowledge in a data mining process. The knowledge is originally stored in data (data is a representation format of knowledge). Unfortunately, we can not read, understand, or use it, since we can not understand data. With this understanding of data mining, we proposed a data-driven knowledge acquisition method based on rough sets. It also improved the performance of classical knowledge acquisition methods. In fact, we also find that the domain-driven data mining and user-driven data mining do not conflict with our data-driven data mining. They could be integrated into domain-oriented data-driven data mining. It is just like the views of data base. Users with different views could look at different partial data of a data base. Thus, users with different tasks or objectives wish, or could discover different knowledge (partial knowledge) from the same data base. However, all these partial knowledge should be originally existed in the data base. So, a domain-oriented data-driven data mining method would help us to extract the knowledge which is really existed in a data base, and really interesting and actionable to the real world.

New judging model of fuzzy cluster optimal dividing based on rough sets theory

To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.

Fuzzy Sets and Rough Sets:a Comparison through an Extension of Obtulowicz's Category

This paper is a purely mathematical one dealing with a common possible foundation of Fuzzy Set Theory and Rough Set Theory.It begins with a generalization of Obtulowicz's paper,rough sets and Heyting algebra valued sets,published in Bull.Polish Acad Sc.(math),198.In this paper Obtulowicz proposes a special subcategory

Machine intelligence,rough sets and rough-fuzzy granular computing:uncertainty handling in bio-informatics and Web intelligence

Machine intelligence,is out of the system by the artificial intelligence shown.It is usually achieved by the average computer intelligence.Rough sets and Information Granules in uncertainty management and soft computing and granular computing is widely used in many fields,such as in protein sequence analysis and biobasis determination,TSM and Web service classification Etc.

NEW METHOD FOR MEASURING FUZZINESS IN ROUGH SETS

A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.

Traffic Flow Data Forecasting Based on Interval Type-2 Fuzzy Sets Theory

This paper proposes a long-term forecasting scheme and implementation method based on the interval type-2 fuzzy sets theory for traffic flow data. The type-2 fuzzy sets have advantages in modeling uncertainties because their membership functions are fuzzy. The scheme includes traffic flow data preprocessing module, type-2 fuzzification operation module and long-term traffic flow data forecasting output module, in which the Interval Approach acts as the core algorithm. The central limit theorem is adopted to convert point data of mass traffic flow in some time range into interval data of the same time range (also called confidence interval data) which is being used as the input of interval approach. The confidence interval data retain the uncertainty and randomness of traffic flow, meanwhile reduce the influence of noise from the detection data. The proposed scheme gets not only the traffic flow forecasting result but also can show the possible range of traffic flow variation with high precision using upper and lower limit forecasting result. The effectiveness of the proposed scheme is verified using the actual sample application. © 2014 Chinese Association of Automation.

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.

基于Rough sets和Fuzzy sets理论的约简算法

对决策表约简的一些roughsets和fuzzysets相关概念进行了阐述。在应用Rough集对决策系统进行约简的基础上,结合模糊聚类分析方法,论述了这一可行的决策表约简算法。该算法以属性核与属性重要性的代数定义形式为基础,利用聚类分析的模糊处理方法,解决了约简过程。并给出了对一电器公司全国连锁销售数据约简处理结果,得出了能帮助不同级别决策者进行决策的辅助性的规则知识。

Rough similarity degree and rough close degree in rough fuzzy sets and the applications

Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.

Fuzzy rough sets in Sostak sense

In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.

Rough Sets Probabilistic Data Association Algorithm and its Application in Multi-target Tracking

A rough set probabilistic data association(RS-PDA)algorithm is proposed for reducing the complexity and time consumption of data association and enhancing the accuracy of tracking results in multi-target tracking application.In this new algorithm,the measurements lying in the intersection of two or more validation regions are allocated to the corresponding targets through rough set theory,and the multi-target tracking problem is transformed into a single target tracking after the classification of measurements lying in the intersection region.Several typical multi-target tracking applications are given.The simulation results show that the algorithm can not only reduce the complexity and time consumption but also enhance the accuracy and stability of the tracking results.

The Solution to Poor Data Bank Using Rough Sets Theory

This article states the poor database which is very common when being used them. So the demanding database must be all-round, effective collection. When the offering database is poor database, it will affect the application of Supporter Deciding. To this question, the author brings out one solution to solve the poor database basing on the Rough Sets Theory. It can scientifically, correctly, effectively supplement the poor database, and can offer greatly help to enforce the application of data and artificial intelligence.

基于Rough Sets的传感器异常数据处理

在各种传感器的应用中,经常要对传感器的测量数据进行处理,以保证测量结果的可靠性．为了利用粗糙集理论处理不确定数据的优点,根据粗糙集理论的思想,先由已知测量数据提取出决策表,再进行补全、离散化等预处理,最后进行属性约简并提取出分类规则,对测量数据进行分类,剔除测量数据中的异常数据．实验结果显示该异常数据发现方法比常用的异常数据处理方法更为客观、精确和可靠．

Rough Sets,Their Extensions and Applications

Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge. Despite its recency, the theory and its extensions have been widely applied to many problems, including decision analysis, data mining, intelligent control and pattern recognition. This paper presents an outline of the basic concepts of rough sets and their major extensions, covering variable precision, tolerance and fuzzy rough sets. It also shows the diversity of successful applications these theories have entailed, ranging from financial and business, through biological and medicine, to physical, art, and meteorological.