Abstract
The correlation coefficient (Pearson’s r) is one of the most frequently used tools in statistics. In this paper we propose a correlation coefficient of Atanassov’s intuitionistic fuzzy sets (A-IFSs). It provides the strength of the relationship between A-IFSs and also shows if the considered sets are positively or negatively correlated. Next, the proposed correlation coefficient takes into account not only the amount of information related to the A-IFS data (expressed by the membership and non-membership values) but also the reliability of the data expressed by a so-called hesitation margin.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Atanassov, K.: Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia (Centr. Sci.-Techn. Libr. of Bulg. Acad. of Sci., 1697/84) (1983) (in Bulgarian)
Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg (1999)
Bustince, H., Burillo, P.: Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 74, 237–244 (1995)
Chiang, D.-A., Lin, N.P.: Correlation of fuzzy sets. Fuzzy Sets and Systems 102, 221–226 (1999)
Gersternkorn, T., Manko, J.: Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems 44, 39–43 (1991)
Hong, D.H., Hwang, S.Y.: Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets and Systems 75, 77–81 (1995)
Hong, D.H., Hwang, S.Y.: A note on the correlation of fuzzy numbers. Fuzzy Sets and Systems 79, 401–402 (1996)
Hung, W.L.: Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. Int. Journal of Uncertainty, Fuzziness and Knowledge-Based systems 9(4), 509–516 (2001)
Hung, W.L., Wu, J.W.: Correlation of intuitionistic fuzzy sets by centroid method. Information Sciences 144, 219–225 (2002)
Kendler, K.S., Parnas, J.: Philosophical Issues in Psychiatry: Explanation, Phenomenology, and Nosology. Johns Hopkins University Press, Baltimore (2008)
Liu, S.-T., Kao, C.: Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems 128, 267–275 (2002)
Rodgers, J.L., Nicewander, W.A.: Thirteen Ways to Look at the Correlation Coefficient. The American Statistician 42(1), 59–66 (1988)
Szmidt, E., Kacprzyk, J.: Remarks on some applications of intuitionistic fuzzy sets in decision making. Notes on IFS 2(3), 22–31 (1996c)
Szmidt, E., Kacprzyk, J.: On measuring distances between intuitionistic fuzzy sets. Notes on IFS 3(4), 1–13 (1997)
Szmidt, E., Kacprzyk, J.: Group Decision Making under Intuitionistic Fuzzy Preference Relations. In: IPMU ’98, pp. 172–178 (1998)
Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114(3), 505–518 (2000)
Szmidt, E., Kacprzyk, J.: On Measures on Consensus Under Intuitionistic Fuzzy Relations. In: IPMU 2000, pp. 1454–1461 (2000)
Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)
Szmidt, E., Kacprzyk, J.: Analysis of Consensus under Intuitionistic Fuzzy Preferences. In: Proc. Int. Conf. in Fuzzy Logic and Technology, pp. 79–82. De Montfort Univ. Leicester, UK (2001)
Szmidt, E., Kacprzyk, J.: Analysis of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Preferences. In: Proc. 9th Int. Conf. IPMU 2002, pp. 1859–1865 (2002a)
Szmidt, E., Kacprzyk, J.: An Intuitionistic Fuzzy Set Based Approach to Intelligent Data Analysis (an application to medical diagnosis). In: Abraham, A., Jain, L., Kacprzyk, J. (eds.) Recent Advances in Intelligent Paradigms and Applications, pp. 57–70. Springer, Heidelberg (2002b)
Szmidt, E., Kacprzyk, J.: An Intuitionistic Fuzzy Set Based Approach to Intelligent Data Analysis (an application to medical diagnosis). In: Abraham, A., Jain, L., Kacprzyk, J. (eds.) Recent Advances in Intelligent Paradigms and Applications, pp. 57–70. Springer, Heidelberg (2002c)
Szmidt, E., Kacprzyk, J.: Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. In: IEEE IS’06, pp. 716–721 (2006)
Szmidt, E., Kacprzyk, J.: An Application of Intuitionistic Fuzzy Set Similarity Measures to a Multi-criteria Decision Making Problem. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 314–323. Springer, Heidelberg (2006)
Szmidt, E., Kacprzyk, J.: Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. In: Masulli, F., Mitra, S., Pasi, G. (eds.) WILF 2007. LNCS (LNAI), vol. 4578, pp. 291–297. Springer, Heidelberg (2007)
Szmidt, E., Kacprzyk, J.: A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. In: 2007 IEEE Conf. on Fuzzy Systems, pp. 481–486 (2007a)
Szmidt, E., Kacprzyk, J.: A new approach to ranking alternatives expressed via intuitionistic fuzzy sets. In: Ruan, D., et al. (eds.) Computational Intelligence in Decision and Control, pp. 265–270. World Scientific, Singapore (2008)
Szmidt, E., Kacprzyk, J.: Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. In: Rakus-Andersson, E., Yager, R., Ichalkaranje, N., Jain, L.C. (eds.) Recent Advances in decision Making, SCI 222, pp. 7–19. Springer, Heidelberg (2009)
Szmidt, E., Kacprzyk, J.: Ranking of Intuitionistic Fuzzy Alternatives in a Multi-criteria Decision Making Problem. In: Proceedings of the conference: NAFIPS 2009, Cincinnati, USA, June 14-17, IEEE, Los Alamitos (2009)
Szmidt, E., Kukier, M.: Classification of Imbalanced and Overlapping Classes using Intuitionistic Fuzzy Sets. In: IEEE IS’06, London, pp. 722–727 (2006)
Szmidt, E., Kukier, M.: A New Approach to Classification of Imbalanced Classes via Atanassov’s Intuitionistic Fuzzy Sets. In: Wang, H.-F. (ed.) Intelligent Data Analysis: Developing New Methodologies Through Pattern Discovery and Recovery, pp. 85–101. Idea Group, USA (2008)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zeng, W., Li, H.: Correlation coefficient of intuitionistic fuzzy sets. Journal of Industrial Engineering International 3(5), 33–40 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Szmidt, E., Kacprzyk, J. (2010). Correlation of Intuitionistic Fuzzy Sets. In: HĂĽllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-14049-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14048-8
Online ISBN: 978-3-642-14049-5
eBook Packages: Computer ScienceComputer Science (R0)