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Knowledge reduction in intuitionistic fuzzy objective information systems

  • 1.

    School of Mathematical Sciences, Anhui University, Hefei, 230601, China

  • 2.

    School of Management, Hefei University of Technology, Hefei, 230009, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.09.012
  • Received Date: 22 June 2014
  • Accepted Date: 24 October 2014
  • Rev Recd Date: 24 October 2014
  • Publish Date: 30 September 2015
    Abstract

  • Abstract

    The classical rough set theory can not be directly employed to reduce knowledge of intuitionistic fuzzy objective information systems. The dominance relation is introduced to intuitionistic fuzzy objective information systems, and intuitionistic fuzzy rough set model based on dominance relation was established. Then, based on the definition of distribution consistent set and assignment consistent set, the judgment theory and discernibility matrices for distribution reduction and assignment reduction were given, and knowledge reduction methods of intuitionistic fuzzy objective information systems were presented. Finally, an example was given to illustrate the effectiveness of the proposed method.

    Abstract

    The classical rough set theory can not be directly employed to reduce knowledge of intuitionistic fuzzy objective information systems. The dominance relation is introduced to intuitionistic fuzzy objective information systems, and intuitionistic fuzzy rough set model based on dominance relation was established. Then, based on the definition of distribution consistent set and assignment consistent set, the judgment theory and discernibility matrices for distribution reduction and assignment reduction were given, and knowledge reduction methods of intuitionistic fuzzy objective information systems were presented. Finally, an example was given to illustrate the effectiveness of the proposed method.
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    • References(24)
  • [1]
    Pawlak Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356.
    [2]
    Pawlak Z. Rough set theory and its applications in data analysis[J]. Cybernetics and Systems, 1998, 29(7): 661-688.
    [3]
    Greco S, Matarazzo B, Slowinski R. Rough sets theory for multi-criteria decision analysis[J]. European Journal of Operational Research, 2001, 129(1): 1-47.
    [4]
    Pawlak Z, Skowron A. Rough sets: Some extensions[J]. Information Sciences, 2007, 177(1): 28-40.
    [5]
    Chen J K, Li J J. An application of rough sets to graph theory[J]. Information Sciences, 2012, 201: 114-127.
    [6]
    Kryszkiewicz M. Comparative studies of alternative type of knowledge reduction in inconsistent systems[J]. International Journal of Intelligent Systems, 2001, 16(1): 105-120.
    [7]
    Zhang Wenxiu, Mi Jusheng, Wu Weizhi. Knowledge reductions in inconsistent information systems[J]. Journal of Computers, 2003, 26(1): 12-18.
    张文修, 米据生, 吴伟志. 不协调目标信息系统的知识约简[J]. 计算机学报, 2002, 26(1): 12-18.
    [8]
    Mi J S, Wu W Z, Zhang W Z. Approaches to knowledge reduction based on variable precision rough set model[J]. Information Sciences, 2004, 159（3-4）: 255-272.
    [9]
    Xu Weihua, Zhang Wenxiu. Knowledge reductions in inconsistent information systems based on dominance relations[J]. Computer Science, 2006, 33(2): 182-184.
    徐伟华, 张文修. 基于优势关系下不协调目标信息系统的知识约简[J]. 计算机科学, 2006, 33(2): 182-184.
    [10]
    Guan Tao, Feng Boqin. Knowledge reduction methods in fuzzy objective information systems[J]. Chinese Journal of Software, 2004, 15(10): 1 470-1 478.
    管涛, 冯博琴. 模糊目标信息系统上的知识约简方法[J]. 软件学报, 2004, 15(10): 1 470-1 478.
    [11]
    Yuan Xiujiu, Zhang Wenxiu. Attribute reductions in fuzzy inconsistent information systems[J]. Systems Engineering-Theory and Practice, 2004, 24(5): 116-120.
    袁修久, 张文修. 模糊目标信息系统的属性约简[J]. 系统工程理论与实践, 2004, 24(5): 116-120.
    [12]
    Sun B Z, Gong Z T, Chen D G. Fuzzy rough set theory for the interval-valued fuzzy information systems[J]. Information Sciences, 2008, 178(13): 2 794-2 815.
    [13]
    Huang Bing, Zhou Xianzhong, Shi Yingchun. Dominance relation-based VPRSM and its application in Fuzzy objective information systems[J]. Computer Science, 2010, 37(3): 227-229.
    黄兵, 周献中, 史迎春. 优势-模糊目标VPRSM及其应用[J]. 计算机科学, 2010, 37(3): 227-229.
    [14]
    Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8(3): 338-353.
    [15]
    Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Set and Systems, 1986, 20(1): 87-96.
    [16]
    Vlachos L K, Sergiadis G D. Intuitionistic fuzzy information: Applications to pattern recognition[J]. Pattern Recognition Letters, 2007, 28 (2): 197-206.
    [17]
    Dymova L, Sevastjanov P. An interpretation of intuitionistic fuzzy sets in terms of evidence theory: Decision making aspect[J]. Knowledge-Based Systems, 2010, 23 (8): 772-782.
    [18]
    Xu Z S. Intuitionistic preference relations and their application in group decision making[J]. Information Sciences, 2007, 177 (11): 2 363-2 379.
    [19]
    He Y D, Chen Y Y, Zhou L G, et al. Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making[J]. Information Sciences, 2014, 259: 142-159.
    [20]
    Zhou L, Wu W Z. On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators[J]. Information Sciences, 2009, 179(7): 883-898.
    [21]
    Xu Xiaolai, Lei Yingjie, Tan Qiaoying. Intuitionistic fuzzy rough sets based on intuitionistic fuzzy triangel norm[J]. Control and Decision, 2008, 23 (8): 900-904.
    徐小来，雷英杰，谭巧英. 基于直觉模糊三角模的直觉模糊粗糙集[J]. 控制与决策，2008，23（8）：900-904.
    [22]
    Zhang Zhiming, Bai Yunchao, Tian Jingfeng. Intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings[J]. Control and Decision, 2010, 25(9): 1 369-1 373.
    张植明, 白云超, 田景峰. 基于覆盖的直觉模糊粗糙集[J]. 控制与决策, 2010, 25(9): 1 369-1 373.
    [23]
    Huang B, Li H X, Wei D K. Dominance-based rough set model in intuitionistic fuzzy information systems[J]. Knowledge-Based Systems, 2012, 28: 115-123.
    [24]
    Huang B, Li H X, Wei D K, et al. Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems[J]. Information Sciences, 2013, 221: 215-229.
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    [1]
    Pawlak Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356.
    [2]
    Pawlak Z. Rough set theory and its applications in data analysis[J]. Cybernetics and Systems, 1998, 29(7): 661-688.
    [3]
    Greco S, Matarazzo B, Slowinski R. Rough sets theory for multi-criteria decision analysis[J]. European Journal of Operational Research, 2001, 129(1): 1-47.
    [4]
    Pawlak Z, Skowron A. Rough sets: Some extensions[J]. Information Sciences, 2007, 177(1): 28-40.
    [5]
    Chen J K, Li J J. An application of rough sets to graph theory[J]. Information Sciences, 2012, 201: 114-127.
    [6]
    Kryszkiewicz M. Comparative studies of alternative type of knowledge reduction in inconsistent systems[J]. International Journal of Intelligent Systems, 2001, 16(1): 105-120.
    [7]
    Zhang Wenxiu, Mi Jusheng, Wu Weizhi. Knowledge reductions in inconsistent information systems[J]. Journal of Computers, 2003, 26(1): 12-18.
    张文修, 米据生, 吴伟志. 不协调目标信息系统的知识约简[J]. 计算机学报, 2002, 26(1): 12-18.
    [8]
    Mi J S, Wu W Z, Zhang W Z. Approaches to knowledge reduction based on variable precision rough set model[J]. Information Sciences, 2004, 159（3-4）: 255-272.
    [9]
    Xu Weihua, Zhang Wenxiu. Knowledge reductions in inconsistent information systems based on dominance relations[J]. Computer Science, 2006, 33(2): 182-184.
    徐伟华, 张文修. 基于优势关系下不协调目标信息系统的知识约简[J]. 计算机科学, 2006, 33(2): 182-184.
    [10]
    Guan Tao, Feng Boqin. Knowledge reduction methods in fuzzy objective information systems[J]. Chinese Journal of Software, 2004, 15(10): 1 470-1 478.
    管涛, 冯博琴. 模糊目标信息系统上的知识约简方法[J]. 软件学报, 2004, 15(10): 1 470-1 478.
    [11]
    Yuan Xiujiu, Zhang Wenxiu. Attribute reductions in fuzzy inconsistent information systems[J]. Systems Engineering-Theory and Practice, 2004, 24(5): 116-120.
    袁修久, 张文修. 模糊目标信息系统的属性约简[J]. 系统工程理论与实践, 2004, 24(5): 116-120.
    [12]
    Sun B Z, Gong Z T, Chen D G. Fuzzy rough set theory for the interval-valued fuzzy information systems[J]. Information Sciences, 2008, 178(13): 2 794-2 815.
    [13]
    Huang Bing, Zhou Xianzhong, Shi Yingchun. Dominance relation-based VPRSM and its application in Fuzzy objective information systems[J]. Computer Science, 2010, 37(3): 227-229.
    黄兵, 周献中, 史迎春. 优势-模糊目标VPRSM及其应用[J]. 计算机科学, 2010, 37(3): 227-229.
    [14]
    Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8(3): 338-353.
    [15]
    Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Set and Systems, 1986, 20(1): 87-96.
    [16]
    Vlachos L K, Sergiadis G D. Intuitionistic fuzzy information: Applications to pattern recognition[J]. Pattern Recognition Letters, 2007, 28 (2): 197-206.
    [17]
    Dymova L, Sevastjanov P. An interpretation of intuitionistic fuzzy sets in terms of evidence theory: Decision making aspect[J]. Knowledge-Based Systems, 2010, 23 (8): 772-782.
    [18]
    Xu Z S. Intuitionistic preference relations and their application in group decision making[J]. Information Sciences, 2007, 177 (11): 2 363-2 379.
    [19]
    He Y D, Chen Y Y, Zhou L G, et al. Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making[J]. Information Sciences, 2014, 259: 142-159.
    [20]
    Zhou L, Wu W Z. On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators[J]. Information Sciences, 2009, 179(7): 883-898.
    [21]
    Xu Xiaolai, Lei Yingjie, Tan Qiaoying. Intuitionistic fuzzy rough sets based on intuitionistic fuzzy triangel norm[J]. Control and Decision, 2008, 23 (8): 900-904.
    徐小来，雷英杰，谭巧英. 基于直觉模糊三角模的直觉模糊粗糙集[J]. 控制与决策，2008，23（8）：900-904.
    [22]
    Zhang Zhiming, Bai Yunchao, Tian Jingfeng. Intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings[J]. Control and Decision, 2010, 25(9): 1 369-1 373.
    张植明, 白云超, 田景峰. 基于覆盖的直觉模糊粗糙集[J]. 控制与决策, 2010, 25(9): 1 369-1 373.
    [23]
    Huang B, Li H X, Wei D K. Dominance-based rough set model in intuitionistic fuzzy information systems[J]. Knowledge-Based Systems, 2012, 28: 115-123.
    [24]
    Huang B, Li H X, Wei D K, et al. Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems[J]. Information Sciences, 2013, 221: 215-229.
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