Induced Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet integral operators and their application in decision making

AbstractBased on the Choquet integral and the generalized Shapley function, two new induced Atanassov's interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet geometric mean (IGS-IVIFHCGM) operator. These operators do not only globally consider the importance of elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, some important cases are examined, and some desirable properties are studied. Furthermore, if the information about the weighting vectors is incompletely known, the models for the optimal λ–fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under Atanassov...

[1]  Zeshui Xu,et al.  Generalized aggregation operators for intuitionistic fuzzy sets , 2010 .

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

[3]  Dimitar Filev,et al.  On the issue of obtaining OWA operator weights , 1998, Fuzzy Sets Syst..

[4]  M. Grabisch.  Fuzzy integral in multicriteria decision making , 1995 .

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

[6]  Jun Wang,et al.  Knowledge Sharing Model based on Concept Clustering , 2007 .

[7]  Guiwu Wei,et al.  Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making , 2010, Appl. Soft Comput..

[8]  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).

[9]  Michel Grabisch,et al.  K-order Additive Discrete Fuzzy Measures and Their Representation , 1997, Fuzzy Sets Syst..

[10]  Hui Li,et al.  The induced continuous ordered weighted geometric operators and their application in group decision making , 2009, Comput. Ind. Eng..

[11]  Zeshui Xu,et al.  Projection Models for Intuitionistic Fuzzy Multiple Attribute Decision Making , 2010, Int. J. Inf. Technol. Decis. Mak..

[12]  Zeshui Xu,et al.  Induced uncertain linguistic OWA operators applied to group decision making , 2006, Inf. Fusion.

[13]  Z. S. Xu,et al.  An overview of operators for aggregating information , 2003, Int. J. Intell. Syst..

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

[15]  Zeshui Xu,et al.  Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information , 2010, Int. J. Intell. Syst..

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

[17]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

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

[19]  Robert Fullér,et al.  An Analytic Approach for Obtaining Maximal Entropy Owa Operator Weights , 2001, Fuzzy Sets Syst..

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

[21]  Qing-wei Cao,et al.  An ILOWG operator based group decision making method and its application to evaluate the supplier criteria , 2011, Math. Comput. Model..

[22]  Ying-Ming Wang,et al.  A preemptive goal programming method for aggregating OWA operator weights in group decision making , 2007, Inf. Sci..

[23]  Montserrat Casanovas,et al.  The Induced Generalized Hybrid Averaging Operator and its Application in Financial Decision Making , 2009 .

[24]  Gleb Beliakov,et al.  Learning Weights in the Generalized OWA Operators , 2005, Fuzzy Optim. Decis. Mak..

[25]  Robert Fullér,et al.  On Obtaining Minimal Variability Owa Operator Weights , 2002, Fuzzy Sets Syst..

[26]  Jean-Luc Marichal,et al.  The influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making , 2000, Discret. Appl. Math..

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

[28]  Ying Luo,et al.  Two new models for determining OWA operator weights , 2007, Comput. Ind. Eng..

[29]  Chunqiao Tan,et al.  A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS , 2011, Expert Syst. Appl..

[30]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[31]  Huayou Chen,et al.  Continuous generalized OWA operator and its application to decision making , 2011, Fuzzy Sets Syst..

[32]  Chunqiao Tan,et al.  Group decision making with linguistic preference relations with application to supplier selection , 2011, Expert Syst. Appl..

[33]  Chunqiao Tan,et al.  Generalized intuitionistic fuzzy geometric aggregation operator and its application to multi-criteria group decision making , 2011, Soft Comput..

[34]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

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

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

[37]  Byeong Seok Ahn,et al.  The uncertain OWA aggregation with weighting functions having a constant level of orness , 2006, Int. J. Intell. Syst..

[38]  K. Atanassov.  Operators over interval valued intuitionistic fuzzy sets , 1994 .

[39]  Ronald R. Yager.  On a semantics for neural networks based on fuzzy quantifiers , 1992, Int. J. Intell. Syst..

[40]  L. Shapley.  A Value for n-person Games , 1988 .

[41]  Jian Lin,et al.  Some hybrid weighted averaging operators and their application to decision making , 2014, Inf. Fusion.

[42]  Michel Grabisch,et al.  p-Symmetric Fuzzy Measures , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[43]  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..

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

[45]  R. Mesiar,et al.  Aggregation operators: new trends and applications , 2002 .

[46]  Zeshui Xu,et al.  Induced generalized intuitionistic fuzzy operators , 2011, Knowl. Based Syst..

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

[48]  Ali Emrouznejad,et al.  Improving minimax disparity model to determine the OWA operator weights , 2010, Inf. Sci..

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

[50]  Zeshui Xu,et al.  Dependent uncertain ordered weighted aggregation operators , 2008, Inf. Fusion.

[51]  M. Grabisch.  The application of fuzzy integrals in multicriteria decision making , 1996 .

[52]  Xiaohong Chen,et al.  Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making , 2011, Int. J. Intell. Syst..

[53]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[54]  Zeshui Xu,et al.  Intuitionistic Fuzzy Information Aggregation: Theory and Applications , 2013 .

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