Interval‐valued probabilistic hesitant fuzzy set and its application in the Arctic geopolitical risk evaluation

The probabilistic hesitant fuzzy set (PHFS) associates the probability with the hesitant fuzzy set (HFS), which has been proposed to improve the granularity of the HFS and can remain more information, is significant to solve the multicriteria group decision‐making (MCGDM) problems when the decision makers fail to provide their preferences completely. To express the probability information existing in the hesitancy more conveniently, we propose a generalized form of P‐HFS named interval‐valued probabilistic hesitant fuzzy set (IVPHFS). In addition, we define some basic operation laws and aggregation operators of IVPHFSs. Based on which, we provide an efficient approach to deal with the practical MCGDM problems by IVPHFSs aggregation operators under the interval‐valued probabilistic hesitant fuzzy environment. Last but not least, we apply the proposed approach to the research of the Arctic geopolitical risk evaluation. The method based on the score function of the probabilistic dual hesitant fuzzy set is also introduced for comparison. The comparing results demonstrate that our approach is more reasonable and logical.

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

[2]  Yuanfang Chen,et al.  Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information , 2014, J. Intell. Fuzzy Syst..

[3]  Francisco Herrera,et al.  Hesitant Fuzzy Sets: State of the Art and Future Directions , 2014, Int. J. Intell. Syst..

[4]  Zeshui Xu,et al.  Operations and integrations of probabilistic hesitant fuzzy information in decision making , 2017, Inf. Fusion.

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

[6]  Wenyi Zeng,et al.  Note on distance measure of hesitant fuzzy sets , 2015, Inf. Sci..

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

[8]  Guiwu Wei,et al.  Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making , 2013, Knowl. Based Syst..

[9]  Guiwu Wei,et al.  Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information , 2009, Knowledge and Information Systems.

[10]  B. Farhadinia,et al.  Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets , 2013, Inf. Sci..

[11]  Ren Zhang,et al.  Comparisons of probabilistic linguistic term sets for multi-criteria decision making , 2017, Knowl. Based Syst..

[12]  Xiaoyue Liu,et al.  Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making , 2014, J. Intell. Fuzzy Syst..

[13]  Feng Fu,et al.  Approaches to multiple attribute decision making with hesitant interval-valued fuzzy information under correlative environment , 2014, J. Intell. Fuzzy Syst..

[14]  Zeshui Xu,et al.  Probabilistic dual hesitant fuzzy set and its application in risk evaluation , 2017, Knowl. Based Syst..

[15]  Yu Zhang,et al.  Research on the computer network security evaluation based on the DHFHCG operator with dual hesitant fuzzy information , 2015, J. Intell. Fuzzy Syst..

[16]  Zeshui Xu,et al.  Hesitant Fuzzy Sets Theory , 2014, Studies in Fuzziness and Soft Computing.

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

[18]  Ting-Zhu Huang,et al.  A Relaxed Splitting Preconditioner for the Incompressible Navier-Stokes Equations , 2012, J. Appl. Math..

[19]  Zhiming Zhang,et al.  A decision support model for group decision making with hesitant multiplicative preference relations , 2014, Inf. Sci..

[20]  Fanyong Meng,et al.  Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures , 2015, Cognitive Computation.

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

[22]  Jun Ye.  Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets , 2010 .

[23]  Zeshui Xu,et al.  Dual Hesitant Fuzzy Sets , 2012, J. Appl. Math..

[24]  Mohammad Izadikhah,et al.  An algorithmic method to extend TOPSIS for decision-making problems with interval data , 2006, Appl. Math. Comput..

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

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

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

[28]  Zhongliang Yue,et al.  An extended TOPSIS for determining weights of decision makers with interval numbers , 2011, Knowl. Based Syst..

[29]  Ren Zhang,et al.  Interval‐valued probabilistic linguistic term sets in multi‐criteria group decision making , 2018, Int. J. Intell. Syst..

[30]  Weihua Gui,et al.  A Hybrid Multiobjective Differential Evolution Algorithm and Its Application to the Optimization of Grinding and Classification , 2013, J. Appl. Math..

[31]  Humberto Bustince,et al.  Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms , 2014, Inf. Sci..