Compound Distance Function for Similarity Measurement Between Fuzzy Sets
Department of Information Technology, University of Miskolc, H-3515 Miskolc-Egyetemváros, Hungary
Distance is usually used to measure the similarity of different objects. The distance function has a key role in clustering, pattern recognition, in information retrieval. The compound real valued distance function on fuzzy sets we propose considers both key aspects of fuzzy sets – membership function and support set.
-  L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.
-  V. G. Adelson and E. Landis, “An algorithm for the organisation of information,” Doklady Akademii Nauk, SSR, pp. 146-263, 1962.
-  P.-N. Yianilos, “Data structures and algorithms for nearest neighbor search in general metric spaces,” Proc. of SODA, pp. 311-321, 1993.
-  A. Anderson, “General Balanded Tree,” J. of Algorithms, 30, pp. 1-18, 1999.
-  Z. C. Johanyák, “Fuzzy Rule Interpolation based on Subsethood Values,” Proc. of 2010 IEEE Int. Conf. on Systems Man and Cybernetics, pp. 2387-2393, 2010.
-  L. T. Kóczy and K. Hirota, “Approximate reasoning by linear rule interpolation and general approximation,” Int. J. of Approximative Reasoning, pp. 197-225, 1993.
-  P. Baranyi, L. T. Kóczy, and T. D. Gedeon, “A Generalized Concept for Fuzzy Rule Interpolation,” IEEE Trans. on Fuzzy Systems, Vol.12, No.6, pp. 820-837, 2004.
-  D. Huttenlocher, G. Klanderman, A. Gregory, and W. Rucklidge, “Comparing Images Using the Hausdorff Distance,” IEEE Trans. on Pattern Analysis and Machine Intelligence, pp. 850-863, 1993.
-  B. Huffaker, M. Fomenkov, D. Plummer, and D. Moore, “Distance Metrics in the Internet,” IEEE Int. Telecommunications Symposium, pp. 200-212, 2002.
-  D. Dubois and H. Prade, “Operations on fuzzy numbers,” Int. J. of Systems Science, Vol.9, No.6, pp. 613-626, 1978.
-  B. Sridevi and R. Nadarajan, “Fuzzy similarity Measure for Generalized Fuzzy Members,” Int. J. Open Problems Compt.Math., Vol.2, No.2, pp. 240-254, June 2009.