Abstract
In 2011 Fullér et al. [An improved index of interactivity for fuzzy numbers, Fuzzy Sets and Systems, 165 (2011), pp. 50–60] introduced a new measure of interactivity between fuzzy numbers (interpreted as possibility distributions), called the weighted possibilistic correlation coefficient, which can be determined from their joint possibility distribution. They also left two questions open regarding the lower limit of the weighted possibilistic correlation coefficient of marginal possibility distribution with the same membership function. In this paper we will answer these questions not only in the case of fuzzy numbers, but also for quasi fuzzy numbers.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Fullér, R., Mezei, J., Várlaki, P.: An improved index of interactivity for fuzzy numbers. Fuzzy Sets Syst. 165, 50–60 (2011). https://doi.org/10.1016/j.fss.2010.06.001
Carlsson, C., Fullér, R., Majlender, P.: On possibilistic correlation. Fuzzy Sets Syst. 155, 425–445 (2005). https://doi.org/10.1016/j.fss.2005.04.014
Fullér, R., Majlender, P.: On interactive fuzzy numbers. Fuzzy Sets Syst. 143, 355–369 (2004). https://doi.org/10.1016/S0165-0114(03)00180-5
Harmati, I.Á.: A note on f-weighted possibilistic correlation for identical marginal possibility distributions. Fuzzy Sets Syst. 165, 106–110 (2011). https://doi.org/10.1016/j.fss.2010.11.005
Hong, D.H., Kim, J.D.: The lower limit for possibilistic correlation coefficient. Appl. Math. Sci. 9(121), 6041–6047 (2015)
Liu, S.T., Kao, C.: Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets Syst. 128, 267–275 (2002)
Hong, D.H.: Fuzzy measures for a correlation coefficient of fuzzy numbers under \(T_W\) (the weakest t-norm)-based fuzzy arithmetic operations. Inf. Sci. 176, 150–160 (2006)
Vaidyanathan, V.S.: Correlation of triangular fuzzy variables using credibility theory. Int. J. Comput. Cognit. 8, 21–23 (2010)
Fan, D., Song, L.: On fuzzy correlation analysis. In: Third International Symposium on Intelligent Information Technology Application Workshops, pp. 372–375. Nanchang (2009). https://doi.org/10.1109/IITAW.2009.92
Thavaneswaran, A., Appadoo, S.S., Paseka, A.: Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing. Math. Comput. Model. 49(1), 352–368 (2009)
Zhang, X., Zhang, W., Xiao, W.W.: Multi-period portfolio optimization under possibility measures. Econ. Model. 35, 401–408 (2013)
Campuzano, F., Mula, J., Peidro, D.: Fuzzy estimations and system dynamics for improving supply chains. Fuzzy Sets Syst. 161(11), 1530–1542 (2010)
He, Y.: An uncertainty visualization technique using possibility theory: possibilistic marching cubes. Int. J. Uncertain. Quantif. 5, 433–451 (2015)
Acknowledgements
The authors are grateful to Prof. László Szeidl of Institute of Applied Mathematics, Óbuda University, Hungary for his helpful comments on probabilistic correlation.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Harmati, I.Á., Fullér, R. (2019). On the Lower Limit for Possibilistic Correlation Coefficient with Identical Marginal Possibility Distributions. In: Kóczy, L., Medina-Moreno, J., Ramírez-Poussa, E. (eds) Interactions Between Computational Intelligence and Mathematics Part 2. Studies in Computational Intelligence, vol 794. Springer, Cham. https://doi.org/10.1007/978-3-030-01632-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-01632-6_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01631-9
Online ISBN: 978-3-030-01632-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)