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The problem of handling imprecision, vagueness and uncertainty in data has been attempted for a long time by philosophers, logicians and mathematicians. Recently there have been many approaches explored to understand and manipulate the imprecise knowledge. The most successful one is fuzzy set theory proposed by Zadeh. The theory of Rough set is a relatively new mathematical approach to decision making...
Rough set theory, proposed by Pawlak, has been proved to be a mathematical tool to deal with vagueness and uncertainty in intelligent information processing. In this paper, we propose the concept of knowledge granulation in interval-valued information systems, and discuss some important properties. From these properties, it can be shown that the proposed knowledge granulation provides important approaches...
In the paper, the concept of rough information entropy is proposed. The monotony between the uncertainty of knowledge in the rough set theory and its corresponding rough entropy is proved. The rough entropy of the uncertainty of ordinary set and fuzzy set, and the monotonous relation between the uncertainty of these two kinds of set and their corresponding rough entropy, are discussed. Using the concept...
An Accurate, Fast and Noise-Adaptive segmentation of Brain MR Images for clinical Analysis is a challenging problem. An improved Hybrid Clustering Algorithm is presented here, which integrates the concept of recently popularized Rough Sets and that of Fuzzy Sets. The concept of lower and upper approximations of rough sets is incorporated to handle uncertainty, vagueness, and incompleteness in class...
In this paper, rough set and evidence theory are applied to the research on the evaluation of group decision making. Focal element increases rapidly while applying the evidence theory. A feature reduction algorithm based on rough set is used when classification result is almost invariable. On one hand, in order to reduce the interdependence between evidences, we adopt a little attributes to evaluation...
In this paper, we first define the concepts of covering decision systems and their reducts. We then develop a sufficient and necessary condition for attribute reduction and construct the dicernibility matrix of attribute reduction, by which we can compute all the reducts of covering decision systems. Finally, an example is employed to illustrate our idea in this paper.
In this paper, we apply classification system denoted Belief Rough Set Classifier (BRSC) based on the hybridization of belief functions and rough sets to learn decision rules from uncertain data consisting of web usage. The uncertainty appears only in decision attributes and is handled by the Transferable Belief Model (TBM), one interpretation of the belief function theory. The web usage mining dataset...
Rough set theory is an important technique for knowledge discovery in databases. The measurement of the uncertainty of knowledge is one of the important issues in rough set theory. The definitions of entropy and the conditional entropy in the process of probability are given, and the meanings of entropy and the conditional entropy are explained in this paper. In addition, the new definition of the...
Rough sets and fuzzy sets are frameworks for the representation of uncertainty. They have been used in various applications such as the imprecise querying of crisp data, uncertainty management in databases, the mining of spatial data, and measurement of information content. This paper discusses such advances in rough and fuzzy set information systems.
The extension of classical rough set model is a very hot and interesting topic. In this paper, our aim is to present the first type of graded rough set (FGRS) based on rough membership function. The concepts of k-regions, k-rough degree, etc., are proposed firstly, and some of important properties are investigated in this rough set model. Moreover, the model has the corresponding properties with classical...
It is well-known to us that the Pawlak's rough set theory, an effective tool to deal with uncertainty and granularity in information systems, is based on equivalence relation. However, in some situations, those conditions of equivalence relation are hardly met. In this paper, we define a new type of upper and lower approximations of rough set in partially ordered sets and propose the reducible element...
Uncertainty plays an important role in clustering. For example in customer segmentation we may be faced with the situation that a certain customer not necessarily belongs to just one segment, i.e. his/her class assignment is uncertain. Several cluster algorithms have been proposed that employ uncertainty modeling in different ways. The most frequently used techniques are probability theory, fuzzy...
Post-classification comparison is a common approach used for multi-sensor remote sensed imagery change detection in practice because it not only minimizes the impacts of sensor difference between multi-temporal images but also detect the detailed `from-to' change while many other techniques can only detect `change/non-change' information. But this approach also presents some well-known limitations,...
The rough fuzzy sets (RFS) is a combination granular computing model with rough sets and fuzzy sets. Its uncertainty includes roughess, rough entropy, fuzziness and fuzzy entropy, etc.. In this paper, the changes of roughness, cut-set and fuzziness are discussed according to the knowledge granularity in different knowledge granularity levels in apporiximation spaces of rough fuzzy sets. Hence, the...
In this paper, by the research of covering rough set theory, rough-vague set model based on covering is presented by integrating rough set theory and vague set theory. Covering rough-vague set is a generalized model of rough set. In order to measure the model's uncertainty perfectly, firstly, we must consider the uncertainty produced by granular size of covering. So knowledge capacity measurement...
Now ontology has been widely used by Artificial Intelligence as an explicit specification of conceptualization in various areas, such as conceptual modeling, information integration, agent-based system design, and semantic web. In this paper, we introduce rough set theory to Ontology. It extends the uncertainty representation in domain ontology and supports uncertainty reasoning. It is more flexible...
Uncertainty information is in many information processing systems, such as data integration system, and expert systems, and so on. There is a contradiction, reasoning detailed information on system requirements can be the most accurate results, while the expert system input is uncertain. So how to reason using uncertain information, and get good results, is our main concern, but also the field of...
In this paper we consider security issues that arise in imprecise databases based on rough set theory. The aspect of security considered is similar to that in statistical databases for which a combination of queries cannot reveal exact values of attributes. Information theory measures are used to characterize security for imprecise databases.
Rough set theory has been considered as a useful tool to deal with inexact, uncertain, or vague knowledge. In real-world, most of information systems are based on dominance relations, called ordered information systems. Although some uncertainty measures to evaluate the uncertainty of rough sets have been investigated in ordered information systems, the existing measures are not able to characterize...
In conventional influence diagrams, the numerical models of uncertainty and imprecise knowledge from large-scaled data set is involved in the systems, the suitability of probability distributions is questioned. The influence diagrams model based on rough sets are proposed in this paper. In the framework, the causal relationships among the nodes and the decision rules are expressed with rough set theory...
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