Geometric Bonferroni means of interval-valued intuitionistic fuzzy numbers and their application to multiple attribute group decision making

The aim of the paper was to propose the interval-valued intuitionistic fuzzy geometric Bonferroni mean and the weighted interval-valued intuitionistic fuzzy geometric Bonferroni mean for aggregating interval-valued intuitionistic fuzzy sets, taking into account the interrelationship between interval-valued intuitionistic fuzzy arguments. Then, some useful properties and special cases of the developed operators are investigated. Furthermore, the developed operators are used to put forward an approach for multiple attribute group decision making with interval-valued intuitionistic fuzzy information. Finally, an illustrative example is furnished to show the feasibility and practicality of the developed approach.

[1]  Peide Liu,et al.  The trapezoid fuzzy linguistic Bonferroni mean operators and their application to multiple attribute decision making , 2012 .

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

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

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

[5]  Zeshui Xu,et al.  Generalized intuitionistic fuzzy Bonferroni means , 2012, Int. J. Intell. Syst..

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

[7]  Xu Ruoning,et al.  Extensions of the analytic hierarchy process in fuzzy environment , 1992 .

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

[9]  Tien-Chin Wang,et al.  Developing a fuzzy TOPSIS approach based on subjective weights and objective weights , 2009, Expert Syst. Appl..

[10]  Zeshui Xu,et al.  A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy bonferroni means , 2011 .

[11]  Zeshui Xu,et al.  Power-Geometric Operators and Their Use in Group Decision Making , 2010, IEEE Transactions on Fuzzy Systems.

[12]  Zeshui Xu,et al.  The continuous ordered weighted geometric operator and its application to decision making , 2006, Fuzzy Sets Syst..

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

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

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

[16]  Ronald R. Yager,et al.  Generalized OWA Aggregation Operators , 2004, Fuzzy Optim. Decis. Mak..

[17]  Ronald R. Yager,et al.  OWA aggregation over a continuous interval argument with applications to decision making , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  J. Merigó,et al.  The Induced Generalized OWA Operator , 2009, EUSFLAT Conf..

[19]  Zeshui Xu,et al.  Uncertain Bonferroni Mean Operators , 2010, Int. J. Comput. Intell. Syst..

[20]  Francisco Herrera,et al.  The ordered weighted Geometric operator: properties and application in MCDM problems , 2000 .

[21]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[22]  Wei Zhou,et al.  Intuitionistic Fuzzy Geometric Bonferroni Means and Their Application in Multicriteria Decision Making , 2012, Int. J. Intell. Syst..

[23]  Ronald R. Yager,et al.  The power average operator , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[24]  Ronald R. Yager,et al.  On generalized Bonferroni mean operators for multi-criteria aggregation , 2009, Int. J. Approx. Reason..

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

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

[27]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

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

[29]  Robert McCartney,et al.  Reasoning with geometric information in digital space , 2005, Knowl. Based Syst..

[30]  Xiaosheng Wu,et al.  An Effective Approach towards Contour-Shape Retrieval , 2007 .

[31]  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).

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

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

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

[35]  G. Wei,et al.  Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making , 2013 .

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

[37]  G. Wei,et al.  Some Geometric Aggregation Operators Based on Interval-Valued Intuitionistic Fuzzy Sets and their Application to Group Decision Making , 2007 .