Abstract
Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawbacks for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature.
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
Preview
Unable to display preview. Download preview PDF.
References
Chen, S.J., Chen, S.M.: A new simple center-of-gravity method for handling the fuzzy ranking and the defuzzification problems. In: 8th National Conf. Fuzzy Theory Applications, Taipei, Republic of China (2000)
Chen, S.J., Chen, S.M.: Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Fuzzy Syst. 11, 45–56 (2003)
Chen, S.J., Chen, S.M.: Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl. Intell. 26, 1–11 (2007)
Chen, S.M.: Operations on fuzzy numbers with function principle. Tamkang J. Manage. Sc. 6, 13–25 (1985)
Chen, S.M.: New methods for subjective mental workload assessment and fuzzy risk analysis. Cybernet. Syst. 27, 449–472 (1996)
Chen, S.M.: Ranking generalized fuzzy number with graded mean integration. In: Proceedings of IFSA 1999, vol. 2, pp. 899–902 (1999)
Gomathi Nayagam, V.L., Sivaraman, G.: A novel similarity measure between generalized fuzzy numbers. Int. J. Comput. Theor. Eng. 4, 448–450 (2012)
Jiménez, A., Mateos, A., Sabio, P.: Dominance intensity measure within fuzzy weight oriented MAUT: an application. OMEGA 41, 397–405 (2013)
Ross, T.J.: Fuzzy logic with engineering applications. John Wiley & Sons, Chichester (2010)
Sridevi, B., Nadarajan, R.: Fuzzy similarity measure for generalized fuzzy numbers. Int. J. Open Probl. Comput. Sc. Math. 2, 111–116 (2009)
Tran, L., Dukstein, L.: Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Set. Syst. 130, 331–341 (2002)
Wei, S.H., Chen, S.M.: A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Syst. Appl. 36, 589–598 (2009)
Xu, Z., Shang, S., Qian, W., Shu, W.: A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers. Expert Syst. Appl. 37, 1920–1927 (2010)
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)
Zhang, W.R.: Knowledge representation using linguistic fuzzy relations. PhD. Dissertation, University of South Carolina, USA (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vicente, E., Mateos, A., Jiménez, A. (2013). A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-38658-9_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38657-2
Online ISBN: 978-3-642-38658-9
eBook Packages: Computer ScienceComputer Science (R0)