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Approach to interval-valued intuitionistic fuzzy multiple attribute decision making with preference information

  • 1.

    School of Business Administration,Hefei University of Technology, Hefei 230009, China

  • 2.

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

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.12.012
  • Received Date: 12 October 2014
  • Accepted Date: 13 June 2015
  • Rev Recd Date: 13 June 2015
  • Publish Date: 30 December 2015
    Abstract

  • Abstract

    With respect to interval-valued intuitionistic fuzzy multiple attribute decision making problems with preference information on alternatives and unknown weight information, some functions and a new entropy were proposed. To gain the weights of the attributes, a new method was proposed based on the entropy and the deviation between values of the preference and values of the attributes. Next, a formula of interval-valued intuitionistic fuzzy numbers correlation coefficient with attribute weights was defined and then a method for ranking the alternatives was proposed. Finally, the method was used as an example to verify its simplicity and effectiveness.

    Abstract

    With respect to interval-valued intuitionistic fuzzy multiple attribute decision making problems with preference information on alternatives and unknown weight information, some functions and a new entropy were proposed. To gain the weights of the attributes, a new method was proposed based on the entropy and the deviation between values of the preference and values of the attributes. Next, a formula of interval-valued intuitionistic fuzzy numbers correlation coefficient with attribute weights was defined and then a method for ranking the alternatives was proposed. Finally, the method was used as an example to verify its simplicity and effectiveness.
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    • References(18)
  • [1]
    Zadeh L A. Fuzzy set[J].Information and Control,1965, 8(3):338-356.
    [2]
    Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1986,20（1）：87-96.
    [3]
    Atanassov K. Operators over interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1994,64(2):159-174.
    [4]
    Zhang H Y, Zhang W X. Europy of interval-valued fuzzy sets based on distance and its relationship with similarity measure[J]. Knowledge-Based Systems,2009,22(6):449-454.
    [5]
    Xu Z S. On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognition[J].Journal of Southeast University (English Edition),2007,23(1): 139-143.
    [6]
    Bustince H,Burillo P. Correlation of interval-valued intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1995,74(2):237-244.
    [7]
    Hong D H. A note on correlation of interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1998,95(1):113-117.
    [8]
    Mondal T K, Samanta S K. Topology of interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,2001, 119(3):483-494.
    [9]
    Mostaghimi M. Bayesian estimation of a decision using information theory[J]. IEEE Trans on Systems,Man,and Cybernetics: Part A: Systems and Humans,1997,27(4):506-517.
    [10]
    Shuiabi E. Entropy as a measure of operational flexibility[J].European Journal of Operational Research, 2005,165(3):696-707.
    [11]
    Wu J Z. Multicriteria decision making method based on intuitionistic fuzzy weighted entropy[J].Expert Systems with Applications,2011,38(1):916-922.
    [12]
    戚晓雯，梁昌勇，张恩桥，等. 基于熵最大化的区间直觉模糊多属性群决策方法[J].系统工程理论与实践，2011，31（10）：1940-1948.
    [13]
    张英俊，马培军，苏小红，等. 属性权重不确定条件下的区间直觉模糊多属性决策[J]. 自动化学报，2012，38（2）：220-227.
    [14]
    Zhang Q S,Liu F C,et al. Information entropy,similarity measure and inclusion measure of intuitionistic fuzzy sets[J].Information Computing and Applications,2012,37(5):392-398.
    [15]
    卫贵武. 对方案有偏好的区间直觉模糊多属性方法[J].系统工程与电子技术，2009,31（1）：116-120.
    [16]
    陈晓红，戴子敬，刘翔，等. 基于熵和关联系数的区间直觉模糊决策方法[J]. 系统工程与电子技术，2013,35（4）：791-794.
    [17]
    Atanassov K, Gargov G. Interval-valued intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1989,31(3):343-349.
    [18]
    郭效芝. 模糊不确定性度量的讨论及扩展[D].西安：西北大学，2004.
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    [1]
    Zadeh L A. Fuzzy set[J].Information and Control,1965, 8(3):338-356.
    [2]
    Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1986,20（1）：87-96.
    [3]
    Atanassov K. Operators over interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1994,64(2):159-174.
    [4]
    Zhang H Y, Zhang W X. Europy of interval-valued fuzzy sets based on distance and its relationship with similarity measure[J]. Knowledge-Based Systems,2009,22(6):449-454.
    [5]
    Xu Z S. On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognition[J].Journal of Southeast University (English Edition),2007,23(1): 139-143.
    [6]
    Bustince H,Burillo P. Correlation of interval-valued intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1995,74(2):237-244.
    [7]
    Hong D H. A note on correlation of interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1998,95(1):113-117.
    [8]
    Mondal T K, Samanta S K. Topology of interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,2001, 119(3):483-494.
    [9]
    Mostaghimi M. Bayesian estimation of a decision using information theory[J]. IEEE Trans on Systems,Man,and Cybernetics: Part A: Systems and Humans,1997,27(4):506-517.
    [10]
    Shuiabi E. Entropy as a measure of operational flexibility[J].European Journal of Operational Research, 2005,165(3):696-707.
    [11]
    Wu J Z. Multicriteria decision making method based on intuitionistic fuzzy weighted entropy[J].Expert Systems with Applications,2011,38(1):916-922.
    [12]
    戚晓雯，梁昌勇，张恩桥，等. 基于熵最大化的区间直觉模糊多属性群决策方法[J].系统工程理论与实践，2011，31（10）：1940-1948.
    [13]
    张英俊，马培军，苏小红，等. 属性权重不确定条件下的区间直觉模糊多属性决策[J]. 自动化学报，2012，38（2）：220-227.
    [14]
    Zhang Q S,Liu F C,et al. Information entropy,similarity measure and inclusion measure of intuitionistic fuzzy sets[J].Information Computing and Applications,2012,37(5):392-398.
    [15]
    卫贵武. 对方案有偏好的区间直觉模糊多属性方法[J].系统工程与电子技术，2009,31（1）：116-120.
    [16]
    陈晓红，戴子敬，刘翔，等. 基于熵和关联系数的区间直觉模糊决策方法[J]. 系统工程与电子技术，2013,35（4）：791-794.
    [17]
    Atanassov K, Gargov G. Interval-valued intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1989,31(3):343-349.
    [18]
    郭效芝. 模糊不确定性度量的讨论及扩展[D].西安：西北大学，2004.
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