As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given, and an numerical example is provided to demonstrate that the developed approach is both valid and practical.
Supported by the Natural Science Foundation of Higher Education of Jiangsu Province (18KJB110024), the High Training Funded for Professional Leaders of Higher Vocational Colleges in Jiangsu Province (2018GRFX038), Science and Technology Research Project of Nantong Shipping College (HYKY/2018A03)
Venkata R. Decision making in the manufacturing environment, using graph theory and fuzzy multiple attribute decision making methods. Springer-Verlag, London, 2007.
Hosseinzade Z, Pagsuyoin S A, Ponnambalam K, et al. Decision-making in irrigation networks:Selecting appropriate canal structures using multi-attribute decision analysis. Science of the Total Environment, 2017, 601-602:177-185.
Arasteh M A, Shamshirband S, Yee P L. Using multi-attribute decision-making approaches in the selection of a hospital management system. Technology and Health Care, 2017, preprint:1-17.
Bellman R, Zadeh L A. Decision-making in a fuzzy environment. Management Science, 1970, 17(4):B141-B164.
Zadeh L A. Fuzzy sets. Information and Control, 1965, 8:338-353.
Zadeh L A. The concept of a linguistic variable and its application to approximate reasoning. Part I, Ⅱ, Ⅲ. Information Sciences, 1975, 8:199-249.
Dubois D, Prade H. Fuzzy Sets and Systems:Theory and Applications. Academic Press, New York, NY, USA, 1980.
Atanassov K T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986, 20(1):87-96.
Atanassov K T, Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1989, 31(3):343-349.
Xu Z S. A method based on linguistic aggregation operators for group decision making with linguistic perference relations. Information Sciences, 2004, 166(1-4):19-30.
Torra V, Narukawa Y. On hesitant fuzzy sets and decision. The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, 1378-1382.
Torra V. Hesitant fuzzy sets. International Journal of Intelligent Systems, 2010, 25(6):529-539.
Zhu B, Xu Z S, Xia M M. Dual hesitant fuzzy sets. Journal of Applied Mathematics, 2012, Article ID 879629, 13 pages.
Su Z, Xu Z S, Liu H F, et al. Distance and similarity measures for dual hesitant fuzzy sets and their applications in pattern recognition. Journal of Intelligent and Fuzzy Systems, 2015, 29:731-745.
Singh P. Distance and similarity measures for multiple-attribute decision making with dual hesitant fuzzy sets. Computational and Applied Mathematics, 2017, 36(1):111-126.
Chen J J, Huang X J, Tang J. Distance measures for higher order dual hesitant fuzzy sets. Computational and Applied Mathematics, 2018, 37(2):1784-1806.
Wang H J, Zhao X F, Wei G W. Dual hesitant fuzzy aggregation operators in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 2014, 26(5):2281-2290.
Ju Y B, Yang S H, Liu X Y. Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 2014, 27(6):2857-2868.
Xing J Y, Yu R, Zhang G C. Some new Dual hesitant fuzzy power aggregation operator. 2nd International Workshop on Materials Engineering and Computer Sciences (IWMECS 2015), 2015, 688-694.
Ye J. Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making. Applied Mathematical Modelling, 2014, 38:659-666,.
Chen Y, Peng X, Guan G, et al. Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information. Journal of Intelligent & Fuzzy Systems, 2014, 26(5):2547-2556.
Tyagi S K. Correlation coefficient of dual hesitant fuzzy sets and its applications. Applied Mathematical Modelling, 2015, 39(22):7082-7092.
Pathinathan T, Savarimuthu J. Multi-attribute decision making in a dual hesitant fuzzy set using TOPSIS. International Journal of Engineering Science Invention Research & Development, 2015, Ⅱ (Issue I):44-54.
Ren Z, Xu Z, Wang H. Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method. Information Sciences, 2017, 388-389:1-16.
Zhao N, Xu Z S. Entropy measures for dual hesitant fuzzy information. 2015 Fifth International Conference on Communication Systems and Network Technologies, Gwalior, 2015, 1152-1156.
Xu Y, Rui D, Wang H. Dual hesitant fuzzy interaction operators and their application to group decision making. Journal of Industrial and Production Engineering, 2015, 32(4):273-290.
Xu Y P. Model for evaluating the mechanical product design quality with dual hesitant fuzzy information. Journal of Intelligent and Fuzzy Systems, 2016, 30:1-6.
Ju Y B, Liu X Y, Yang S H. Interval-valued dual hesitant fuzzy aggregation operators and their applications to multiple attribute decison making. Journal of Intelligent & Fuzzy Systems, 2014, 27:1203-1218.
Qu G H, Qu W H, Li C H. Some new interval-valued dual hesitant fuzzy Choquet integral aggregation operators and their applications. Journal of Intelligent & Fuzzy Systems, 2018, 34(1):245-266.
Qua G, Zhou H, Qu W, et al. Shapley interval-valued dual hesitant fuzzy Choquet integral aggregation operators in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 2018, 34(3):1827-1845.
Zang Y, Zhao X, Li S. Interval-valued dual hesitant fuzzy Heronian mean aggregation operators and their applications to multi-attribute decison making. International Journal of Computational Intelligence and Applications, 2018, 17(1):1-26.
Zhang W K, Li X, Ju Y B, Some aggregation operators based on Einstein operations under intervalvalued dual hesitant fuzzy setting and their application. Mathematical Problems in Engineering, 2014, Artical ID:958927, 12 pages.
Hamacher H. Uber logische verknunpfungrnn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione. in:Trappl, Klir, Riccardi (Eds.), Progress in Cybernatics and Systems Research, Hemisphere, Washington DC, 1978, 3:276-288.
Xia M M, Xu Z S, Zhu B. Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowledge-Based Systems, 2012, 31:78-88.
Xu Z S. On consistency of the weighted geometric mean complex judgement marix in AHP. European Journal of Operational Research, 2000, 126:683-687.
Beliakov G, Pradera A, Calov T. Aggregation functions:A guide for practitioners. Springer, Heidelberg, Berlin, New York, 2007.
Yager R R. On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Fuzzy Systems, 2004, 12:45-61.
Xu Z S, Da Q L. The ordered weighted geometic averaging operators. International Journal of Intelligent Systems, 2002, 17:709-716.
Xu Z S. Uncertain Multiple Attribute Decision Making:Meathods and Application. Tsinghua University Press, Beijing, China, 2004.