Combination Entropy and Combination Granulation in Rough Set Theory

Qian, Yuhua; Liang, Jiye

doi:10.1142/s0218488508005121

Cited by 153 publications

(94 citation statements)

References 11 publications

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“…To overcome this limitation, we modify formula (8) based on the idea of combination entropy and combination granulation [42,45], and the definition of combined fuzzinessbased uncertainty measure is as follows.…”

Section: Modified Uncertainty Measure Of Rough Fuzzy Setsmentioning

confidence: 99%

Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance

Yang

Zhao

2018

Mathematical Problems in Engineering

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As an extension of Pawlak's rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak's rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is proposed. Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed. Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty. Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes. These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence.

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Section: Modified Uncertainty Measure Of Rough Fuzzy Setsmentioning

confidence: 99%

Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance

Yang

Zhao

2018

Mathematical Problems in Engineering

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“…Therefore, feature selection techniques have been extensively studied in the past decades. Some well-known techniques, such as attribute frequency of discernibility matrix (Guan et al 2007;Wang and Wang 2001;Zhang et al 2003aZhang et al , 2003bZhang et al , 2003c, positive region, i.e., dependence (Chouchoulas and Shen 2001;Modrzejewski 1993), mutual information (Peng et al 2005;Slezak 2002), consistency method (Dash and Liu 2003), various information entropy reduction (Slezak 2002;Liang and Xu 2002;Qian and Liang 2008), have been developed based on this optimal algorithm. Zhang et al (2003a,b,c) proposed an algorithm based on the discernibility matrix, which employed appearing frequency of attribute as heuristic information to select attributes and eliminate redundant attributes whose time complexity was O(|C| 2 |U | 2 ).…”

Section: Related Workmentioning

confidence: 99%

“…proposed a new conditional information entropy that can reflect the change of the condition attributes distribution in the process of reduction with respect to the positive region and presented a new representation of attribute reduction. Qian and Liang (2008) presented the definitions of the conditional combination entropy and the mutual information, researched several useful properties, and built a heuristic function in the heuristic reduction algorithm with respect to combination entropy.…”

Section: Related Workmentioning

confidence: 99%

Bidirectional heuristic attribute reduction based on conflict region

Long-shu

et al. 2014

Soft Comput

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Attribute reduction is one of the key issues in rough set theory. Many heuristic reduction strategies such as forward heuristic reduction, backward heuristic reduction and for-backward heuristic reduction have been proposed to obtain a subset of attributes which has the same discernibility as the original attribute set. However, some methods are usually computationally time consuming for large data sets. Therefore, this paper focuses on solving the attribute reduction efficiency in the decision system. We first introduce the quotient of approximation, positive region and conflict region, and then research the heuristic reduction algorithm based on conflict region. Sequentially, we put forward to a mechanism of bidirectional heuristic attribute reduction based on conflict region quotient and design a bidirectional heuristic attribute reduction algorithm. Finally, the experimental results with UCI data sets show that the proposed reduction algorithm is an effective technique to deal with large high-dimensional data sets.

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“…Therefore, some heuristic algorithms that can find one reduct in a shorter time were proposed in Refs. [11,13,24,25,39,43,45,46,48], most of which are greedy and forward search algorithms. Starting with a nonempty set, these search algorithms keep adding one or several attributes of high significance into a pool at each iteration until the dependence no longer increases.…”

Section: Reduction Algorithm To Small Granularitymentioning

confidence: 99%

“…These two attribute reduction algorithms are usually computationally very expensive, especially for dealing with large-scale data sets of high dimensions. Therefore, to overcome this difficulty, many heuristic attribute reduction algorithms have been developed in rough set theory [11,13,24,25,39,35,43,45,46,48]. A heuristic attribute reduction algorithm can extract a single reduct from a given table in a relatively short time.…”

Section: Introductionmentioning

confidence: 99%

An efficient rough feature selection algorithm with a multi-granulation view

Liang

Wang

Dang

et al. 2012

International Journal of Approximate Reasoning

Self Cite

158

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Feature selection is a challenging problem in many areas such as pattern recognition, machine learning and data mining. Rough set theory, as a valid soft computing tool to analyze various types of data, has been widely applied to select helpful features (also called attribute reduction). In rough set theory, many feature selection algorithms have been developed in the literatures, however, they are very time-consuming when data sets are in a large scale. To overcome this limitation, we propose in this paper an efficient rough feature selection algorithm for large-scale data sets, which is stimulated from multi-granulation. A sub-table of a data set can be considered as a small granularity. Given a large-scale data set, the algorithm first selects different small granularities and then estimate on each small granularity the reduct of the original data set. Fusing all of the estimates on small granularities together, the algorithm can get an approximate reduct. Because of that the total time spent on computing reducts for sub-tables is much less than that for the original large-scale one, the algorithm yields in a much less amount of time a feature subset (the approximate reduct). According to several decision performance measures, experimental results show that the proposed algorithm is feasible and efficient for large-scale data sets.

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Combination Entropy and Combination Granulation in Rough Set Theory

Cited by 153 publications

References 11 publications

Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance

Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance

Bidirectional heuristic attribute reduction based on conflict region

An efficient rough feature selection algorithm with a multi-granulation view

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