Rough Entropy Research Articles

Uncertainty of Rough Sets in Different Knowledge Granularities

Rougness,rough entropy,fuzziness,and fuzzy entropy are major methods for measuring the uncertainty of rough sets.In different knowledge granularity levels,a hierarchical knowledge space chain is proposed based on the attributes in information systems.Some regularities of the changing of rough entropy and fuzziness of a rough set with the knowledge granularity are found to be inconsistent with human cognition.A new method for measuring the fuzziness of rough sets is proposed based on information entropy.The fuzziness measured by the new method is monotonously decreasing with the refining of knowledge granularity in apporiximation spaces.It overcomes the problem of roughness and rough entropy.Finally,the relations of the changing of roughness and fuzziness are analyzed in different knowledge granularities.

Rough set-derived measures in image classification accuracy assessment

Currently, there are two types of measure in image classification accuracy assessment: pixel-level measures and category-level/map-level measures. These have their own limitations for representing the uncertainty at pixel and category/map levels. In addition, some of these measures derived from the error matrix are obtained by collecting reference data and then they may be affected by factors related to the sampling. This paper uses rough set theory to obtain the rough degree, rough entropy, quality of approximation and accuracy of approximation. Incorporating traditional measures, they compose one kind of three-level architecture for the classified image, which contains pixel-level measures, object/category-level measures and map-level measures. Unlike some conventional measures, these new measures can be derived directly from the supervised classification result without collecting reference data. A case study on the Landsat TM image is used to substantiate the conceptual arguments. The results demonstrate that the proposed measures are valid for measuring the accuracy of classified remotely sensed imagery and can provide additional information to conventional measures.

Ant colony feature selection based on fuzzy rough set information entropy

Most heuristic feature selection algorithms converge easily to local-best, which cannot search the whole feature space effectively. In order to improve the parallel search ability to feature space, the information entropy theory of fuzzy rough set was introduced to ant colony model, and the ant search strategy, pheromone updating and state transition rules of the model have been modified to realize ant colony model based feature selection. UCI datasets experiments indicate that the proposed algorithm is effective to feature subset selection compared with three classical feature selection algorithms.

Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems

In this paper, concepts of knowledge granulation, knowledge entropy and knowledge uncertainty measure are given in ordered information systems, and some important properties of them are investigated. From these properties, it can be shown that these measures provides important approaches to measuring the discernibility ability of different knowledge in ordered information systems. And relationship between knowledge granulation, knowledge entropy and knowledge uncertainty measure are considered. As an application of knowledge granulation, we introduce definition of rough entropy of rough sets in ordered information systems. By an example, it is shown that the rough entropy of rough sets is more accurate than classical rough degree to measure the roughness of rough sets in ordered information systems.

An Enterprise Financial Evaluation Model Based on Rough Set theory with Information Entropy

Enterprise financial evaluation is an important issue. Rough set is a new technique for data mining domain application. Information Entropy, as a measurement of the average amount of information contained in an information system, is used in the classification of objectives and the analysis of information systems. In this study, establish a financial evaluation model using rough Information entropy approach. Therefore, we firstly define the attribute reduction based on rough set theory. Secondly, we define information entropy. Using this definition, we can easily find the important of attributes. Thirdly, we discuss the reducible indiscernible matrix and decision rule generation. The empirical research which is based on the latest data of Taiwan’s listed company, the result shows that this method is high accurate. Using the unmatched and unbalanced training data and test data, rough set theory with information entropy, shows the best overall prediction accuracy level at 83.4%.

Intensity of geomagnetic storms depends on the X‐line location in the plasma sheet

Magnetic reconnection in the plasma sheet, known as the near‐Earth X‐line (NEXL), is observed within ∼30 RE from Earth during substorms. In the absence of substorms, the reconnection X‐line is observed beyond ∼30 RE, denoted as mid‐distant‐tail X‐line (MDXL). During quasi‐periodic substorms, convection is enhanced by the NEXL to intensify the ring current of major storms with Dst < ∼ −100 nT. During extended periods without substorms, convection is driven by the MDXL to intensify the ring current of minor storms with Dst > ∼ −100 nT. Motivated by observations, we propose a ring current injection conjecture to order the storm intensity: Ring current intensity increases if the X‐line forms closer to Earth. We carry out a rough entropy analysis as a first step toward theoretical investigation of the ring current injection conjecture. We show that substorm‐associated near‐Earth reconnection of closed plasma sheet field lines cannot provide the ring current particles for a major magnetic storm. However, we find that near‐Earth reconnection of tail lobe field lines in a few strong substorm events could provide the particles for the storm‐time ring current, if the X‐line is located earthward of ∼15 RE with an uncertainty up to ∼25 RE.

Histogram Thresholding using Beam Theory and Ambiguity Measures

This paper presents a novel histogram thresholding technique based on the beam theory of solid mechanics and the minimization of ambiguity in information. First, a beam theory based histogram modification process is carried out. This beam theory based process considers a distance measure in order to modify the shape of the histogram. The ambiguity in the overall information given by the modified histogram is then minimized to obtain the threshold value. The ambiguity minimization is carried out using the theories of fuzzy and rough sets, where a new definition of rough entropy is presented. The applications of the proposed scheme in performing object and edge extraction in images are reported and compared with those of a few existing classical and ambiguity minimization based schemes for thresholding. Experimental results are given to demonstrate the effectiveness of the proposed method in terms of both qualitative and quantitative measures.

Information entropy, rough entropy and knowledge granulation in incomplete information systems

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances that are characterized by vagueness and uncertainty. Rough set theory uses a table called an information system, and knowledge is defined as classifications of an information system. In this paper, we introduce the concepts of information entropy, rough entropy, knowledge granulation and granularity measure in incomplete information systems, their important properties are given, and the relationships among these concepts are established. The relationship between the information entropy E(A) and the knowledge granulation GK(A) of knowledge A can be expressed as E(A)+GK(A) = 1, the relationship between the granularity measure G(A) and the rough entropy E r(A) of knowledge A can be expressed as G(A)+E r(A) = log2|U|. The conclusions in Liang and Shi (2004) are special instances in this paper. Furthermore, two inequalities − log2 GK(A) ≤ G(A) and E r(A) ≤ log2(|U|(1 − E(A))) about the measures GK, G, E and E r are obtained. These results will be very helpful for understanding the essence of uncertainty measurement, the significance of an attribute, constructing the heuristic function in a heuristic reduct algorithm and measuring the quality of a decision rule in incomplete information systems.

Granular computing, rough entropy and object extraction

The problem of image object extraction in the framework of rough sets and granular computing is addressed. A measure called “rough entropy of image” is defined based on the concept of image granules. Its maximization results in minimization of roughness in both object and background regions; thereby determining the threshold of partitioning. Methods of selecting the appropriate granule size and efficient computation of rough entropy are described.

THE INFORMATION ENTROPY, ROUGH ENTROPY AND KNOWLEDGE GRANULATION IN ROUGH SET THEORY

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.

Rough reduction in algebra view and information view

Rough set (RS) is a valid theory to deal with imprecise, uncertain, and vague information. It has been applied successfully since it was developed by Professor Z. Pawlak in 1982 in such fields as machine learning, data mining, intelligent data analyzing, control algorithm acquiring, etc. The greatest advantage of the RS is its great ability to compute the reductions of information systems. Many researchers have done a lot of work in developing efficient algorithms to compute useful reductions of information systems. There also are some researchers working on the relationship between rough entropy and information entropy. They have developed some efficient reduction algorithms based on conditional information entropy. In this article, the relationship of the definitions of rough reduction in algebra view and information view is studied. Some relationships such as inclusion relationship under some conditions and equivalence relationship under some other conditions are presented. The inclusion relationship between the attribute importance defined in algebra view and information view is presented also. Some efficient heuristic reduction algorithms can be developed further using these results. © 2003 Wiley Periodicals, Inc.

THE ALGORITHM ON KNOWLEDGE REDUCTION IN INCOMPLETE INFORMATION SYSTEMS

Rough set theory is emerging as a powerful tool for reasoning about data, knowledge reduction is one of the important topics in the research on rough set theory. It has been proven that finding the minimal reduct of an information system is a NP-hard problem, so is finding the minimal reduct of an incomplete information system. Main reason of causing NP-hard is combination problem of attributes. In this paper, knowledge reduction is defined from the view of information, a heuristic algorithm based on rough entropy for knowledge reduction is proposed in incomplete information systems, the time complexity of this algorithm is O(|A|2|U|). An illustrative example is provided that shows the application potential of the algorithm.

Information-theoretic measures of uncertainty for rough sets and rough relational databases

Rough set theory has become well-established as a mechanism for uncertainty management in a wide variety of applications including databases. This paper addresses the measurement of uncertainty in rough sets and rough relational databases by introducing a measurement based on information theory. This rough entropy is discussed as it applies to rough sets in general, and in particular to aspects of the rough relational database model.