Abstract
Engineering management plays an important role in the socio-economic field, where complex and uncertain factors usually exist. Dual hesitant fuzzy sets (DHFSs) are powerful tools to denote the decision makers’ uncertain and hesitant preferences. Correlation measures and correlation coefficients are two important types of indices in decision making. This paper focuses on correlation measures and correlation coefficients for DHFSs and their application in engineering management. To do this, two dual hesitant fuzzy correlation coefficients are defined, and their properties are studied. Considering the situation where interactive characteristics among elements exist, two Shapley correlation coefficients are defined. When the weighting information is incompletely known, models for the optimal two-additive measures are built. Then, an algorithm to clustering analysis and decision making with incomplete weighting information and interactive characteristics are presented, respectively. Two corresponding examples about real estate investment and engineering cost management are offered to demonstrate the application of the approaches.
Similar content being viewed by others
References
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Baroni M, Barthelemy F, Mokrane M (2007) Using rents and price dynamics in real estate portfolio valuation. Property Management 25(5):462–486
Bonizzoni P, Vedova GD, Dondi R, Jiang T (2005) Correlation clustering and consensus clustering. In: 16th International conference on algorithms and computation, pp 226–235
Bozorgi A (2015) Integrating value and uncertainty in the energy retrofit analysis in real estate investment—next generation of energy efficiency assessment tools. Energ Effi 8(5):1015–1034
Chen N, Xu ZS, Xia MM (2013a) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211
Chen N, Xu ZS, Xia MM (2013b) Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 37:528–540
Chen ZC, Liu PH, Pei Z (2015) An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int J Comput Intell Syst 8(4):747–760
Chiang DA, Lin NP (1999) Correlation of fuzzy sets. Fuzzy Sets Syst 102(2):221–226
Du YQ, Hou FJ, Zafar W, Yu Q, Zhai YB (2017) A novel method for multiattribute decision making with interval-valued pythagorean fuzzy linguistic information. Int J Intell Syst 32(10):1085–1112
Dumitrescu D (1978) Fuzzy correlation. Studia Univ Babes Bolyai Math 23:41–44
Geipele I, Kauškale L (2013) The influence of real estate market cycle on the development in Latvia. Proc Eng 57:327–333
Grabisch M (1997) k-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst 92(2):167–189
Herrera F, Martinez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752
Hung WL (2001) Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. Int J Uncertain Fuzziness Knowl-Based Syst 9(4):509–516
Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv (CSUR) 31(3):264–323
Karnik NN, Mendel JM (2001) Operations on type-2 fuzzy sets. Fuzzy Sets Syst 122(2):327–348
Kauškale L, Geipele I (2017) Integrated approach of real estate market analysis in sustainable development context for decision making. Proc Eng 172:505–512
Li HZ, Lang B (2008) The application of the whole life cycle engineering cost management on the electricity engineering field. J N China Electric Power Univ 1:7–11
Liao HC, Xu ZS, Zeng XJ (2015a) Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowl-Based Syst 82:115–127
Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015b) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst 76:127–138
Liu PD (2013) Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans Fuzzy Syst 22(1):83–97
Liu PD (2018) Two-dimensional uncertain linguistic generalized normalized weighted geometric Bonferroni mean and its application to multiple-attribute decision making. Sci Iran Trans E Ind Eng 25(1):450–465
Liu ST, Kao C (2006) Fuzzy measures for correlation coefficient of fuzzy numbers. Inf Sci 128(2):267–275
Liu PD, Liu JL (2018) Some q-rung orthopair fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. Int J Intell Syst 33(2):315–347
Liu PD, Tang GL (2018) Some intuitionistic fuzzy prioritized interactive Einstein Choquet operators and their application in decision making. IEEE Access 6:72357–72371
Liu PD, Wang P (2018a) Multiple-attribute decision making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst 27(5):1–14
Liu PD, Wang P (2018b) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280
Liu Y, Zhang P (2015) The control of engineering project cost management of construction enterprise based on lean model experimental analysis. In: International conference on intelligent computation technology and automation, IEEE, pp 983–986
Liu PD, Zhang XH (2018) Approach to multi-attributes decision making with intuitionistic linguistic information based on dempster-shafer evidence theory. IEEE Access 6:52969–52981
Liu PD, Chen SM, Wang P (2018) Multiple-attribute group decision-making based on q-rung orthopair fuzzy power maclaurin symmetric mean operators. IEEE Trans Syst Man Cybern Syst 99:1–16
Meng FY, Chen XH (2015a) Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput 7(4):445–463
Meng FY, Chen XH (2015b) Interval-valued intuitionistic fuzzy multi-criteria group decision making based on cross entropy and 2-additive measures. Soft Comput 19(7):2071–2082
Meng FY, Chen XH (2017) Correlation coefficient of interval-valued intuitionistic uncertain linguistic sets and its application. Cybern Syst 48(2):114–135
Meng FY, Tang J (2013) Interval-valued intuitionistic fuzzy multiattribute group decision making based on cross entropy measure and Choquet integral. Int J Intell Syst 28(12):1172–1195
Meng FY, Tan CQ, Zhang Q (2014a) An approach to multi-attribute group decision making under uncertain linguistic environment based on the Choquet aggregation operators. J Intell Fuzzy Syst 26(2):769–780
Meng FY, Chen XH, Zhang Q (2014b) Multi-attribute decision analysis under a linguistic hesitant fuzzy environment. Inf Sci 267:287–305
Meng FY, Wang C, Chen XH (2016) Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput 8(1):52–68
Miyamoto S (2005) Remarks on basics of fuzzy sets and fuzzy multisets. Fuzzy Sets Syst 156(3):427–431
Murthy CA, Pal SK, Majumder DD (1985) Correlation between two fuzzy membership functions. Fuzzy Sets Syst 17:23–38
Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic terms sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119
Ru XL (2009) Discussion on the engineering cost management in the design stage. Sci-Tech Inf Dev Econ 19(4):218–220
Shapley LS (1953) A value for n-person game. In: Kuhn H, Tucker A (eds) Contributions to the theory of games. Princeton University Press, Princeton, pp 307–317
Strembelev S (2015) Arbitrability of disputes about investment in the construction of real estate in Russia. J Mol Endocrinol 22(2):103–111
Sugeno M (1974) Theory of fuzzy integral and its application. Doctorial dissertation, Tokyo Institute of Technology
Szmidt E, Kacprzyk J (2010) Correlation of intuitionistic fuzzy sets. International conference on information processing and management of uncertainty in knowledge-based systems. Springer, Berlin, pp 169–177
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539
Tyagi SK (2015) Correlation coefficient of dual hesitant fuzzy sets and its applications. Appl Math Model 39(22):7082–7092
Wang L, Ni MF, Zhu L (2013) Correlation measures of dual hesitant fuzzy sets. Journal of Applied Mathematics 2013:1–12
Xu ZS (2006) On correlation measures of intuitionistic fuzzy sets. In: IDEAL’06 proceedings of the 7th international conference on international data engineering and automated learning, Springer, Berlin, pp 16–24
Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394
Ye J (2014) Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making. Appl Math Model 38(2):659–666
Yu CH (1993) Correlation of fuzzy numbers. Fuzzy Sets Syst 55(3):303–307
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zeng P (2007) Engineering cost management in bidding period of construction enterprises. Shanxi Archit 33(19):249–250
Zhou SJ, Wang F, Li YC (2009) Application of PPC model based on RAGA in real estate investment decision-making. Engineering 1(2):106–110
Zhu B, Xu ZS, Xia MM (2012) Dual hesitant fuzzy sets. J Appl Math 11:2607–2645
Acknowledgements
This work was supported by the National Natural Science Foundation of China (nos. 71571192, and 71874112), the Beijing Intelligent Logistics System Collaborative Innovation Center (no. 2018KF-06), the Major Project for National Natural Science Foundation of China (no. 71790615), and the State Key Program of National Natural Science of China (no. 71431006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Meng, F., Xu, Y. & Wang, N. Correlation coefficients of dual hesitant fuzzy sets and their application in engineering management. J Ambient Intell Human Comput 11, 2943–2961 (2020). https://doi.org/10.1007/s12652-019-01435-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-019-01435-7