Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

[1]  Guiwu Wei,et al.  Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making , 2014, Expert Syst. Appl..

[2]  Carlo Bonferroni Sulle medie multiple di potenze , 1950 .

[3]  Zeshui Xu,et al.  Intuitionistic Fuzzy Bonferroni Means , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Humberto Bustince,et al.  On averaging operators for Atanassov's intuitionistic fuzzy sets , 2011, Inf. Sci..

[5]  Zeshui Xu,et al.  Hesitant fuzzy geometric Bonferroni means , 2012, Inf. Sci..

[6]  Ronald R. Yager,et al.  Generalized Bonferroni mean operators in multi-criteria aggregation , 2010, Fuzzy Sets Syst..

[7]  Zeshui Xu,et al.  Interval-valued hesitant preference relations and their applications to group decision making , 2013, Knowl. Based Syst..

[8]  Deng-Feng Li,et al.  TOPSIS-Based Nonlinear-Programming Methodology for Multiattribute Decision Making With Interval-Valued Intuitionistic Fuzzy Sets , 2010, IEEE Transactions on Fuzzy Systems.

[9]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

[10]  Zeshui Xu,et al.  Fuzzy harmonic mean operators , 2009, Int. J. Intell. Syst..

[11]  Na Chen,et al.  Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making , 2011, Group Decision and Negotiation.

[12]  Xiaohong Chen,et al.  Induced choquet ordered averaging operator and its application to group decision making , 2010, Int. J. Intell. Syst..

[13]  Guodong Zhong,et al.  Models for multiple attribute decision making method in hesitant triangular fuzzy setting , 2014, J. Intell. Fuzzy Syst..

[14]  Jing Liu,et al.  Normalized Geometric Bonferroni Operators of Hesitant Fuzzy Sets and Their Application in Multiple Attribute Decision Making , 2013 .

[15]  Guiwu Wei,et al.  Hesitant fuzzy prioritized operators and their application to multiple attribute decision making , 2012, Knowl. Based Syst..

[16]  Xiaohong Chen,et al.  Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making , 2010, Expert Syst. Appl..

[17]  Dejian Yu,et al.  Triangular Hesitant Fuzzy Set and Its Application to Teaching Quality Evaluation , 2013 .

[18]  W. Pedrycz,et al.  A fuzzy extension of Saaty's priority theory , 1983 .

[19]  Zeshui Xu,et al.  Hesitant fuzzy information aggregation in decision making , 2011, Int. J. Approx. Reason..

[20]  S. Chanas The use of parametric programming in fuzzy linear programming , 1983 .

[21]  Michel Grabisch,et al.  A discrete Choquet integral for ordered systems , 2011, Fuzzy Sets Syst..

[22]  Ronald R. Yager,et al.  Prioritized OWA aggregation , 2009, Fuzzy Optim. Decis. Mak..

[23]  Vicenç Torra,et al.  Hesitant fuzzy sets , 2010, Int. J. Intell. Syst..

[24]  Qingguo Li,et al.  Generalized hesitant fuzzy prioritized Einstein weighted averaging operator and its application in group decision making , 2013, 2013 International Conference on Fuzzy Theory and Its Applications (iFUZZY).

[25]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[26]  G. Klir,et al.  Fuzzy Measure Theory , 1993 .

[27]  Zeshui Xu,et al.  Hesitant fuzzy Bonferroni means for multi-criteria decision making , 2013, J. Oper. Res. Soc..

[28]  R. Weiner Lecture Notes in Economics and Mathematical Systems , 1985 .

[29]  Gui-Wu Wei,et al.  GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting , 2010, Knowl. Based Syst..

[30]  Qingguo Li,et al.  Multiple Attribute Decision Making Based on Hesitant Fuzzy Einstein Geometric Aggregation Operators , 2014, J. Appl. Math..

[31]  Chunqiao Tan,et al.  Induced choquet ordered averaging operator and its application to group decision making , 2010 .

[32]  Zeshui Xu,et al.  Geometric Bonferroni means with their application in multi-criteria decision making , 2013, Knowl. Based Syst..

[33]  Dejian Yu,et al.  Generalized Hesitant Fuzzy Bonferroni Mean and Its Application in Multi-criteria Group Decision Making ⋆ , 2012 .

[34]  Ting-Yu Chen,et al.  Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis , 2010, Inf. Sci..

[35]  G. Choquet Theory of capacities , 1954 .

[36]  Yejun Xu,et al.  The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making , 2012, Appl. Soft Comput..

[37]  Li-Jun Wang,et al.  Triangular fuzzy Bonferroni mean operators and their application to multiple attribute decision making , 2015, J. Intell. Fuzzy Syst..