Study on the ranking problems in multiple attribute decision making based on interval‐valued intuitionistic fuzzy numbers

This paper puts forward a new ranking method for multiple attribute decision‐making problems based on interval‐valued intuitionistic fuzzy set (IIFS) theory. First, the composed ordered weighted arithmetic averaging operator and composed ordered weighted geometric averaging operator are extended to the IIFSs in which they are, respectively, named interval‐valued intuitionistic fuzzy composed ordered weighted arithmetic averaging (IIFCOWA) operator and interval‐valued intuitionistic composed ordered weighted geometric averaging (IIFCOWG) operator. Afterwards, to compare interval‐valued intuitionistic fuzzy numbers, we define the concepts of the maximum, the minimum, and ranking function. Some properties associated with the concepts are investigated. Using the IIFCOWA or IIFCOWG operator, we establish the detailed steps of ranking alternatives (or attributes) in multiple attribute decision making. Finally, an illustrative example is provided to show that the proposed ranking method is feasible in multiple attribute decision making.

[1]  K. Atanassov.  More on intuitionistic fuzzy sets , 1989 .

[2]  Dimitar Filev,et al.  Induced ordered weighted averaging operators , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[3]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[4]  Z. S. Xu,et al.  Models for Multiple Attribute Decision Making with Intuitionistic Fuzzy Information , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[5]  Zeshui Xu,et al.  An overview of methods for determining OWA weights , 2005, Int. J. Intell. Syst..

[6]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[7]  Jun Ye,et al.  Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment , 2009, Expert Syst. Appl..

[8]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[9]  Zeshui Xu,et al.  On Geometric Aggregation over Interval-Valued Intuitionistic Fuzzy Information , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

[10]  Xuelan Zeng,et al.  A New Priority Method for Triangular Fuzzy Number Complementary Judgment Matrix , 2007, Third International Conference on Natural Computation (ICNC 2007).

[11]  Ronald R. Yager,et al.  Induced aggregation operators , 2003, Fuzzy Sets Syst..

[12]  Z. S. Xu,et al.  The uncertain OWA operator , 2002, Int. J. Intell. Syst..

[13]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[14]  Xu Ze-shui.  A Fuzzy Ordered Weighted Geometric Operator and Its Application in Fuzzy AHP , 2002 .

[15]  Jian Jhen Chen,et al.  Approach to Group Decision Making Based on Interval-Valued Intuitionistic Judgment Matrices , 2007 .

[16]  Francisco Herrera,et al.  Multiperson decision-making based on multiplicative preference relations , 2001, Eur. J. Oper. Res..

[17]  Z. Xu,et al.  Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making , 2007 .

[18]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[19]  Z. S. Xu,et al.  The ordered weighted geometric averaging operators , 2002, Int. J. Intell. Syst..

[20]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[21]  DA Qing-li.  Uncertain ordered weighted geometric averaging operator and its application to decision making , 2005 .

[22]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[23]  K. Atanassov,et al.  Interval-Valued Intuitionistic Fuzzy Sets , 2019, Studies in Fuzziness and Soft Computing.