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Positive domain reduction in intuitionistic fuzzy objective information systems

  • 1.

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

  • 2.

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

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.04.011
  • Received Date: 12 September 2014
  • Accepted Date: 29 December 2014
  • Rev Recd Date: 29 December 2014
  • Publish Date: 30 April 2015
    Abstract

  • Abstract

    The classical rough set theory can not be directly used to reduce knowledge for intuitionistic fuzzy objective information systems. To solve this problem, dominance relation was firstly introduced to intuitionistic fuzzy objective information systems, and intuitionistic fuzzy rough set based on dominance relation was defined. Then, the notion of the relative positive domain and the significance of attributes in classical rough set theory were generalized to intuitionistic fuzzy objective information systems, while the monotone property of the relative positive domain was investigated. According to the different characteristics of attributes and the definition of positive domain reduction, the judgment theorem for positive domain reduction was given, the positive domain reduction algorithm using attribute significance as heuristic information was presented, and the complexity analysis of the algorithm was given. Finally, the effectiveness of the proposed algorithm was illustrated with comparative experiments.

    Abstract

    The classical rough set theory can not be directly used to reduce knowledge for intuitionistic fuzzy objective information systems. To solve this problem, dominance relation was firstly introduced to intuitionistic fuzzy objective information systems, and intuitionistic fuzzy rough set based on dominance relation was defined. Then, the notion of the relative positive domain and the significance of attributes in classical rough set theory were generalized to intuitionistic fuzzy objective information systems, while the monotone property of the relative positive domain was investigated. According to the different characteristics of attributes and the definition of positive domain reduction, the judgment theorem for positive domain reduction was given, the positive domain reduction algorithm using attribute significance as heuristic information was presented, and the complexity analysis of the algorithm was given. Finally, the effectiveness of the proposed algorithm was illustrated with comparative experiments.
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    • References(19)
  • [1]
    Pawlak Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356.
    [2]
    Pawlak Z, Skowron A. Rough sets: Some extensions[J]. Information Sciences, 2007, 177(1): 28-40.
    [3]
    张文修, 梁怡, 吴伟志. 信息系统与知识发现[M]. 北京: 科学出版社, 2003.
    [4]
    Yang X B, Yang J Y, Wu C, et al. Dominance-based rough set approach and knowledge reductions in incomplete ordered information systems[J]. Information Sciences, 2008, 178(4): 1219-1234.
    [5]
    Qian Y H, Dang C Y, Liang J Y, et al. Set-valued ordered information systems[J]. Information Sciences, 2009, 179(16): 2809-2832.
    [6]
    Li H X, Zhou X Z, Zhao J B, et al. Non-monotonic attribute reduction in decision-theoretic rough sets[J]. Fundamenta Informaticae, 2013, 126(4): 415-432.
    [7]
    Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of General System, 1990, 17(2-3): 191-209.
    [8]
    Jensen R, Shen Q. Fuzzy-rough attribute reduction with application to web categorization[J]. Fuzzy Sets and Systems, 2004, 141(3): 469-485.
    [9]
    Cornelis C, Jensen R, Hurtado. G, et al. Attribute selection with fuzzy decision reducts[J]. Information Sciences, 2010, 180(2): 209-224.
    [10]
    Chen D G, Zhao S Y. Local reduction of decision system with fuzzy rough sets[J]. Fuzzy Sets and Systems, 2010, 161(13): 1871-1883.
    [11]
    Atanassov K T. Intuitionistic fuzzy sets[J]. Fuzzy Set and Systems, 1986, 20(1): 87-96.
    [12]
    Atanassov K T, Gargor G. Interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1989, 31(3): 343-349.
    [13]
    Zhou L, Wu W Z, Zhang W X. On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators[J]. Information Sciences, 2009, 179(7): 883-898.
    [14]
    Zhou L, Wu W Z. Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory[J]. Computers and Mathematics with Applications, 2011, 62(1): 282-296.
    [15]
    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, 2009, 23(8): 900-904.
    Xu X L, Lei Y J, Tan Q Y. Intuitionistic fuzzy rough sets based on intuitionistic fuzzy triangle norm[J]. Control and Decision, 2009, 23(8): 900-904.
    [16]
    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.
    [17]
    Huang B, Wei D K,Li H X, 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.
    [18]
    Xu Z S. Intuitionistic preference relations and their application in group decision making[J]. Information Sciences, 2007, 177(11): 2363-2379.
    [19]
    Vlachos I K, Sergiadis G D. Subsethood, entropy, and cardinality for interval-valued fuzzy sets-A algebraic derivation[J]. Fuzzy Sets and Systems, 2007, 158(12): 1384-1396.
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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, Skowron A. Rough sets: Some extensions[J]. Information Sciences, 2007, 177(1): 28-40.
    [3]
    张文修, 梁怡, 吴伟志. 信息系统与知识发现[M]. 北京: 科学出版社, 2003.
    [4]
    Yang X B, Yang J Y, Wu C, et al. Dominance-based rough set approach and knowledge reductions in incomplete ordered information systems[J]. Information Sciences, 2008, 178(4): 1219-1234.
    [5]
    Qian Y H, Dang C Y, Liang J Y, et al. Set-valued ordered information systems[J]. Information Sciences, 2009, 179(16): 2809-2832.
    [6]
    Li H X, Zhou X Z, Zhao J B, et al. Non-monotonic attribute reduction in decision-theoretic rough sets[J]. Fundamenta Informaticae, 2013, 126(4): 415-432.
    [7]
    Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of General System, 1990, 17(2-3): 191-209.
    [8]
    Jensen R, Shen Q. Fuzzy-rough attribute reduction with application to web categorization[J]. Fuzzy Sets and Systems, 2004, 141(3): 469-485.
    [9]
    Cornelis C, Jensen R, Hurtado. G, et al. Attribute selection with fuzzy decision reducts[J]. Information Sciences, 2010, 180(2): 209-224.
    [10]
    Chen D G, Zhao S Y. Local reduction of decision system with fuzzy rough sets[J]. Fuzzy Sets and Systems, 2010, 161(13): 1871-1883.
    [11]
    Atanassov K T. Intuitionistic fuzzy sets[J]. Fuzzy Set and Systems, 1986, 20(1): 87-96.
    [12]
    Atanassov K T, Gargor G. Interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1989, 31(3): 343-349.
    [13]
    Zhou L, Wu W Z, Zhang W X. On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators[J]. Information Sciences, 2009, 179(7): 883-898.
    [14]
    Zhou L, Wu W Z. Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory[J]. Computers and Mathematics with Applications, 2011, 62(1): 282-296.
    [15]
    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, 2009, 23(8): 900-904.
    Xu X L, Lei Y J, Tan Q Y. Intuitionistic fuzzy rough sets based on intuitionistic fuzzy triangle norm[J]. Control and Decision, 2009, 23(8): 900-904.
    [16]
    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.
    [17]
    Huang B, Wei D K,Li H X, 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.
    [18]
    Xu Z S. Intuitionistic preference relations and their application in group decision making[J]. Information Sciences, 2007, 177(11): 2363-2379.
    [19]
    Vlachos I K, Sergiadis G D. Subsethood, entropy, and cardinality for interval-valued fuzzy sets-A algebraic derivation[J]. Fuzzy Sets and Systems, 2007, 158(12): 1384-1396.
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