• Login
  • Register
  • Search

The Distance of Hesitant Interval-valued Fuzzy Sets and its Application in Multi-criteria Decision Making

Jie Qian, Juan-juan Peng

Abstract


In this paper, some operations of hesitant interval-valued fuzzy sets are introduced. Then the corresponding distance measures between two hesitant interval-valued fuzzy numbers is developed, which obtained motivating by the distance for discrete sets, and s ome desirable properties are examined in detail. Furthermore, an approach to multi-criteria decision making with hesitant interval-valued fuzzy information is proposed. Finally, an application of the proposed method is shown to demonstrate its practicality and effectiveness, and the results are compared by utilizing the other existing method.

Keywords


Multiple criteria decision making; hesitant interval-valued fuzzy sets; distance

Full Text:

PDF

Included Database


References


L. A. Zadeh, Fuzzy sets, Information Control 8 (1965) 338–356.

V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems 25 (2010) 529–539.

V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea (2009)1378–1382.

M.M. Xia, Z.S. Xu, Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning 52 (2011) 395–407.

B. Zhu, Z.S. Xu, M.M. Xia, Hesitant fuzzy geometric Bonferoni means, Information Sciences 205 (2012) 72–85.

G.W. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems 31 (2012) 176–182.

M.M. Xia, Z.S. Xu, N. Chen, Some Hesitant fuzzy aggregation operators with their application in group decision making, Group Decision and Negotiation 22(2) ( 2013) 259–279.

D.J. Yu, Y.Y. Wu, W. Zhou, Multi-criteria decision making based on Choquet integral under hesitant fuzzy environment, Journal of Computational Information Systems 12 (2011) 4506–4513.

X. Yang, Z.S. Xu, H.C. Liao, Correlation coefficients of hesitant multiplicative sets and their applications in decision making and clustering analysis, Applied Soft Computing, DOI: http://dx.doi.org/10.1016/j.asoc.2017.08.011, 2017.

Z.S. Xu, M.M. Xia, Distance and similarity measures for hesitant fuzzy sets, Information Sciences 181 (2011) 2128–2138.

Z.S. Xu, M.M. Xia, On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems 26 (2011) 410–425.

N. Chen, Z. S. Xu, M.M. Xia, Interval-valued hesitant preference relation relations and their applications to group decision making, Knowledge-based systems 37 (2013) 528–540.

G.W. Wei, X.F. Zhao, R. Lin, Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making, Journal of Intelligent & Fuzzy Systems 46 (4) (2013) 43–53.

H. Zhang, S. Lan, S. Liao, On interval-valued hesitant fuzzy rough approximation operators, Soft Computing 20 (1) (2016) 189–209.

F. Jin, Z. Ni, H. Chen, Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making, Soft Computing 20 (5) (2016) 1863–1878.

P. Quirós, P. Alonso, H. Bustince et al, An entropy measure definition for finite interval-valued hesitant fuzzy sets, Knowledge-Based Systems 84 (C) (2015) 121–133.

F. Jin, Z. Ni, H. Chen et al, Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures, Computers & Industrial Engineering 101 (2016) 103–115.

S. Darabi, J. Heydari, An interval-valued hesitant fuzzy ranking method based on group decision analysis for green supplier selection, Ifac Papersonline 49 (2) (2016) 12–17.

H. Gitinavard, S. M. Mousavi, B. Vahdani, A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems, Neural Computing and Applications 27 (6) (2016) 1593–1605.

P.Y. Chen, An interval estimation for the number of signals, Signal Processing 85 (3)(2005) 1622–1633.

A. Sengupta, T. K. Pal, On comparing interval numbers, European Journal of Operational Research 127 (1)(2000) 28–43.

Z.S. Xu, Dependent uncertain ordered weighted aggregation operators, Information Fusion 9 (2) (2008) 310–316.

Z.S. Xu, On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives, Fuzzy Optimization and Decision Making 4 (2) (2005) 131–139.

G. Klir, B. Yuan, Fuzzy sets and fuzzy logic:theory and applications,Prentice Hall,Upper Saddle River, N. J. 1995.

H.T. Nguyen, R. A. Walker, A first course in fuzzy logic, CRC press, Boca Raton, Florida,1997.

E.P. Klement, R. Mesiar, Logical, Algebraic, analytic and probabilistic aspects of triangular norms, Elsevier, Amsterdam, 2005.

Z.S. Xu, J. Chen, An overview of distance and similarity measures of intuitionistic fuzzy sets,International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16 (2008) 529–555.

Z.S. Xu, A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making, Group Decision and Negotiation 19 (2010) 57–76.

Z.S. Xu, New method for uncertain multi-attribute decision making problem, Journal of systems engineering 17 (2002) 177–181.

Q. Zhang, P.Z. Fan, D.H. Pan,A ranking approach for intervals numbers in uncertain multiple attribute decision making problems,Engineering-Theory & Practice 19 (1999) 129–133.

L. Tran, L. Duckstein, Comparison of Fuzzy Numbers usinga Fuzzy Distance Measure, Fuzzy Sets and Systems 130 (2002) 331–341.

C. Knauera, M. Loffler, The directed Hausdorff distance between imprecise point sets, Theoretical Computer Science 412 (2011) 4173–4186.




DOI: http://dx.doi.org/10.18686/mmf.v1i2.1049

Refbacks