Generalized Hesitant Fuzzy Generalized Shapley-Choquet Integral Operators and Their Application in Decision Making

In this paper, two generalized hesitant fuzzy generalized Shapley-Choquet integral operators are defined, which globally consider the importance of elements in a set, and the correlations among them. Some important special cases are examined. An improvement order relationship between hesitant fuzzy elements (HFEs) is introduced, and a new distance measure of HFSs is defined. This distance measure can calculate the distance between two HFEs with different lengths. If the information about the weights of attributes is incompletely known, the model for the optimal fuzzy measure on attribute set is established. As a series of development, an approach to hesitant fuzzy multi-attribute decision making with incomplete weight information is developed, and a practical example is provided to verify the developed approach and demonstrate its practicality and effectiveness.

[1]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy sets , 2011, Inf. Sci..

[2]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[3]  Guiwu Wei,et al.  Hesitant Fuzzy Choquet Integral Aggregation Operators and Their Applications to Multiple Attribute Decision Making , 2012 .

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

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

[6]  Thomas Wensing,et al.  Analysis and Optimization , 2011 .

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

[8]  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..

[9]  Aida Azizi,et al.  Selection of optimum maintenance strategies based on a fuzzy analytic hierarchy process , 2014 .

[10]  Ying Wang,et al.  A Method for Hesitant Fuzzy Multiple Attribute Decision Making and Its Application to Risk Investment , 2011 .

[11]  G. Wei,et al.  Extension of VIKOR method for decision making problem based on hesitant fuzzy set , 2013 .

[12]  Ju Wang,et al.  Reasoning within intuitionistic fuzzy rough description logics , 2009, Inf. Sci..

[13]  Zeshui Xu,et al.  On distance and correlation measures of hesitant fuzzy information , 2011, Int. J. Intell. Syst..

[14]  Zeshui Xu,et al.  Hesitant fuzzy entropy and cross‐entropy and their use in multiattribute decision‐making , 2012, Int. J. Intell. Syst..

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

[16]  R. Dorf,et al.  The Balanced Scorecard: Translating Strategy Into Action , 1997, Proceedings of the IEEE.

[17]  Guiwu Wei,et al.  Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making , 2013, J. Intell. Fuzzy Syst..

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

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

[20]  Jian Wu,et al.  The extended COWG operators and their application to multiple attributive group decision making problems with interval numbers , 2011 .

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

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