Granular computing: from granularity optimization to multi-granularity joint problem solving

Wang, Guoyin; Yang, Jie; Ji, Xu

doi:10.1007/s41066-016-0032-3

Cited by 116 publications

(33 citation statements)

References 69 publications

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“…As a new methodology for simulating human cognitive mechanism, granular computing (GrC) is regarded as an umbrella covering the theories, methodologies, techniques, and tools in artificial intelligence [12][13][14][15][16][17]. From the viewpoint of GrC, the certainty and uncertainty of knowledge can be transformed for each other at a certain granularity level [18].…”

Section: Mathematical Problems In Engineeringmentioning

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: Mathematical Problems In Engineeringmentioning

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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“…Rough set [6], an important mathematical tool of granular computing [7], provides an effective method of knowledge discovery [8] and knowledge reduction. Covering rough set [9] and multigranulation rough set are two special models dealing with the real data sets when overlapping and multiple knowledge are involved.…”

Section: Introductionmentioning

confidence: 99%

Relative Reduction of Neighborhood-Covering Pessimistic Multigranulation Rough Set Based on Evidence Theory

You

Wang

2019

Information

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Relative reduction of multiple neighborhood-covering with multigranulation rough set has been one of the hot research topics in knowledge reduction theory. In this paper, we explore the relative reduction of covering information system by combining the neighborhood-covering pessimistic multigranulation rough set with evidence theory. First, the lower and upper approximations of multigranulation rough set in neighborhood-covering information systems are introduced based on the concept of neighborhood of objects. Second, the belief and plausibility functions from evidence theory are employed to characterize the approximations of neighborhood-covering multigranulation rough set. Then the relative reduction of neighborhood-covering information system is investigated by using the belief and plausibility functions. Finally, an algorithm for computing a relative reduction of neighborhood-covering pessimistic multigranulation rough set is proposed according to the significance of coverings defined by the belief function, and its validity is examined by a practical example.

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“…Authors of many papers on GC draw our attention to great difficulties accompanying solving GC-problems and to their high complicacy level. For example, the paper by Wang et al (2017) informs about various levels of a problem analysis on which granules of various precision have to be used to get coarse results (better comprehension, lower precision) or fine results (more difficult comprehension, higher precision). Authors of the paper Kovalerchuk and Kreinovich (2017) show not only how difficult can be solving of granular problems but also how differently the problem solution can be interpreted by people solving it.…”

Section: Introductionmentioning

confidence: 99%

Solving different practical granular problems under the same system of equations

Piegat

Landowski

2017

Granul. Comput.

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This paper contains discussion about the paper of Kreinovich (Granular Computing 1(3): [171][172][173][174][175][176][177][178][179] 2016) in which the author suggests the thesis that in conditions of uncertainty ''solving different practical problems we get different solutions of the same system of equations with the same granules''. Authors of the present paper are of the opinion that the above thesis is result of one-dimensional approach to interval analysis prevailing at present in scientific community and also used by Kreinovich. According to this approach the direct result of any arithmetic operation Ã 2 fþ; À; Â; =g on intervals is also an interval. The main scientific contribution of the paper is showing that a granular problem analysis in an incomplete, low-dimensional space can lead to untrue conclusions because picture of the problem in this space is too poor and part of valuable, important information is lost. What is seen in the fulldimensional space of the problem space cannot be seen in an incomplete, low-dimensional space. The paper also shortly describes a multidimensional approach to interval arithmetic that is free of the above-described deficiencies.

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Granular computing: from granularity optimization to multi-granularity joint problem solving

Cited by 116 publications

References 69 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

Relative Reduction of Neighborhood-Covering Pessimistic Multigranulation Rough Set Based on Evidence Theory

Solving different practical granular problems under the same system of equations

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