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In this paper, a new entropy based uncertainty measure is introduced for evaluating the significance of subsets of attributes in incomplete decision tables. Some properties of rough conditional entropy are derived. And three attribute reduction algorithms are provided, including an algorithm using exhaustive search, an algorithm using heuristic search and an algorithm using probabilistic search for...
Interval-valued information systems are generalized models of single-valued information systems. However, there are few studies on incomplete interval-valued data, which exist in many practical issues. In this paper, we propose a dominance relation for incomplete interval-valued information systems. Based on the dominance relation, the concepts of knowledge information entropy, knowledge rough entropy,...
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...
Uncertainty measures can supply new viewpoints for analyzing data. They can help us in disclosing the substantive characteristics of data. The uncertainty measurement issue is also a key topic in the rough-set theory. Although there are some measures to evaluate the uncertainty for complete decision systems (also called decision tables), they cannot be trivially transplanted into incomplete decision...
Uncertainty is an intrinsic feature of decision-making information systems and thus plays an important role in their performance. The system uncertainty can be measured efficiently by rough group theory based methods, which has better performance and certain drawbacks when combined with entropy. Based on all known entropy and approximation classification quality, we proposed a new measure method which...
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...
During the evaluation of multi-source information system, uncertainty exists widely. In order to use and process the uncertainty and improve the creditability of system evaluation, this paper based on the cloud theory, studied the mapping method between nature variable and quantity variable. At the same time, the paper promoted a novel evaluation method of system performance based on the cloud theory...
In order to measure fuzzy uncertainty of fuzzy rough set, a cross fuzzy entropy (CFE) measuring method based on the notion of rough membership in fuzzy rough set is defined combing with the analysis of fuzzy entropy in fuzzy set, the relative properties are analyzed. This method can not only measure fuzzy uncertainty of fuzzy rough set, but also indirectly reflect rough uncertainty contained in data...
The attribute reduction is a core theory of the rough set theory. It has been proven that computing the optimal reduction of decision table is a NP-hard problem. In the paper here, the application of rough entropy in rough sets theory is analyzed, the uncertainty measure of the importance of attribute in decision table is proposed, then, a heuristic algorithm based on rough entropy for reduction of...
Information granularity is an approache to measuring uncertainty of an information system in granular computing. Partial order relations are often used to characterize the monotonicity of an uncertainty measure. In this paper, we focus on a generalized partial relation ≤' with set-size character to information systems, and prove that three existing partial relations (≤1, ≤2 and ≤3) are all its special...
Rough set theory is a valid mathematical tool to deal with inexact, uncertain, or vague knowledge. 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 well the imprecision of a rough set. In order to find a new method to measure the roughness of rough sets in ordered information...
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...
Real-life data are frequently imperfect: data may be affected by uncertainty, vagueness, and incompleteness. In this paper, based on dominance relation, the concepts of knowledge granulation and rough entropy of imcomplete information system (include missing data and imprecise data) are defined, their important properties are given, and the relationship between those concepts is established. These...
To study the battlefield electromagnetic measurement data effectively, it is very necessary to research a valid attribute reduction method for dealing with the measurement information. Firstly, the deficiencies of some current information entropy models are analyzed, and a new kind of generalized information entropy model based on fuzzy-rough set is proposed, which can introduce the probability distribution...
There are five dimensionalities of information, such as organization, user, administrative levels, technology and time. Using value of information entropy of attribute we can compute the authority of attributes. Then we can monitor the key attributes and forecast the trouble.
The concept of Shannon information entropy is introduced to area of e-commerce. Sorting of significance of attributes in database based on entropy is proposed to discover information value on e-commerce information analysis. The information entropy is also applied to integration of e-commerce to measure betimes, continuity, objectivity and comprehensiveness.
This study proposes a combined entropy weight and TOPSIS method for information system selection. In the present paper, information entropy is employed to derive the objective weights of the evaluation criteria, and a modified TOPSIS method is employed to rank a finite number of feasible alternatives in order of preference and then select a suitable information system that conforms to the decision...
Knowledge in knowledge bases have two categories: complete and incomplete. In this paper, through uniformly expressing these two kinds of knowledge, we first address four operators on a knowledge base, which are adequate for generating new knowledge through using known knowledge. Then, we establish the relationship between knowledge and knowledge granulation. These results will be very helpful for...
Attribute reduction is one of the important topics in the research on rough set theory, it plays an important role in machine learning and data mining. However, is the decision performance of a decision table changed after an attribute reduction? In this paper, we analyze the change of the decision performance through using the positive-region reduction and the Shannon entropy reduction. The change...
Uncertainty measure is a key issue of uncertain systems. In this paper, conditional entropy and increment information are introduced to discuss the two set relations in the same incomplete information systems based on covering approximation space. Two new kinds of measurements about the knowledge of rough set are presented. Furthermore the finer the set is, the lower the conditional entropy and increment...
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