Matrix computation for measuring uncertainty of rough sets

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (29): 42-45.

• 研究、探讨 • Previous Articles Next Articles

Matrix computation for measuring uncertainty of rough sets

XIE Bin1，2，MI Jusheng1，ZHANG Junpeng2

1.College of Mathematics and Information Science，Hebei Normal University，Shijiazhuang 050016，China
2.College of Information Technology，Hebei Normal University，Shijiazhuang 050016，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-10-11 Published:2011-10-11

粗糙集不确定性度量的矩阵运算

解滨1，2，米据生1，张军鹏2

1.河北师范大学数学与信息科学学院，石家庄 050016
2.河北师范大学信息技术学院，石家庄 050016

Abstract

Abstract: As one of the most important issues in rough set theory，roughness and fuzziness of rough sets have been widely studied.An improved method is proposed for measuring the uncertainty of rough sets based on fuzzy theory and granular computing theory.A definition of relative knowledge granulation and a concept of boundary entropy for an information system are given，under which the measure functions of roughness and fuzziness are modified.Both of roughness and fuzziness are monotonously decreasing with the refining of knowledge granularities in approximation spaces.Two matrix algorithms are presented for measuring the roughness and fuzziness of rough sets，which are easy to implement.

Key words: rough sets, uncertainty, knowledge granularities, roughness, fuzziness

摘要： 粗糙集的不确定性度量是粗糙集理论的重要研究内容之一。结合模糊理论和粒计算理论改进了粗糙集的不确定性度量方法。通过集合的相对知识粒度及边界熵给出了粗糙集的粗糙性度量函数与模糊性度量函数，随着近似空间知识粒的细分，粗糙集的粗糙度与模糊度均满足单调递减的性质。利用矩阵理论提出了易于实现的粗糙性度量与模糊性度量的矩阵算法。

关键词: 粗糙集, 不确定性, 知识粒度, 粗糙度, 模糊度

XIE Bin1，2，MI Jusheng1，ZHANG Junpeng2. Matrix computation for measuring uncertainty of rough sets[J]. Computer Engineering and Applications, 2011, 47(29): 42-45.

解滨1，2，米据生1，张军鹏2. 粗糙集不确定性度量的矩阵运算[J]. 计算机工程与应用, 2011, 47(29): 42-45.

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Matrix computation for measuring uncertainty of rough sets

粗糙集不确定性度量的矩阵运算

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