Abstract
In addition to fuzzy and stochastic theory, interval analysis is a powerful tool for solving uncertain problems. An important problem in interval analysis is the ranking of interval numbers. This paper analyzes the definitions of satisfaction index for comparing interval numbers. Sometimes different definitions of the satisfaction indices lead to confusion. The main result of the paper is to show that some existing definitions of the satisfaction index are equivalent.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ishibuchi, H., Tanaka, H.: Formulation and analysis of linear programming problem with interval coefficients. J. Jpn. Ind. Manag. Assoc. 40, 320–329 (1989). (in Japanese)
Facchinetti, G., Ricci, R.G., Muzzioli, S.: Note on ranking fuzzy triangular numbers. J. Int. J. Intell. Syst. 13, 613–622 (1998)
Da, Q.L., Liu, X.W.: Interval number linear programming and its satisfactory solution. J. Syst. Eng. Theory Pract. 19, 3–7 (1999). (in Chinese)
Sengupta, A., Pal, T.K.: On comparing interval numbers. J. Eur. J. Oper. Res. 127, 28–43 (2000)
Sengupta, A., Pal, T.K., Chakraborty, D.: Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. J. Fuzzy Sets Syst. 119, 129–138 (2001)
Liu, Z.X., Zhang, C., Gang, J.T.: Ranking of fuzzy numbers. J. Liaoning Normal Univ. 25, 62–365 (2002)
Xu, Z.S., Da, Q.L.: Possibility degree method for ranking interval numbers and its application. J. Syst. Eng. 18, 67–70 (2003). (in Chinese)
Lan, J.B., Cao, L.J., Lin, J.: Method for ranking interval numbers based on two-dimensional priority degree. J. Chongqing Inst. Technol. (Nat. Sci. Edn.) 21, 63–67 (2007)
Sun, H.L., Yao, W.X.: Comments on methods for ranking interval numbers. J. Syst. Eng. 25, 304–312 (2010). (in Chinese)
Qin, C.Y., Wang, H.P., Li, W.: Satisfaction indices for comparing any two interval numbers, Technical report, Institute of Operational Research & Cybernetics, Hangzhou Dianzi University (2007)
Acknowledgements
This research was supported by the NNSF of China (Grant No. 11701506).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Li, H. (2020). Order Relations Between Interval Numbers. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_81
Download citation
DOI: https://doi.org/10.1007/978-3-030-32456-8_81
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32455-1
Online ISBN: 978-3-030-32456-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)