×

Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images. (English) Zbl 1112.94033

Summary: Two measures are presented for comparing fuzzy sets. The method for constructing these measures is studied, starting from fuzzy DI-subsethood measures [see H. Bustince, V. Mohedano, E. Barrenechea and M. Pagola, “Definition and construction of fuzzy DI-subsethood measures”, Inf. Sci. 176, 3190–3231 (2006; Zbl 1104.03052)]. We then analyze and compare the properties satisfied by the measures and those satisfied by other classical indices used in the literature on fuzzy sets. The minimal set of conditions is studied that, from our point of view, must be met by any given measure for comparing images. We also prove that only one of the identified measures fulfills such conditions. Finally, all the measures studied are applied to different images and the results are analyzed, indicating that measures constructed from fuzzy DI-subsethood measures provide the best results.

MSC:

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
94A17 Measures of information, entropy
68U10 Computing methodologies for image processing
03E72 Theory of fuzzy sets, etc.

Citations:

Zbl 1104.03052
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bandler, W.; Kohout, L., Fuzzy power sets and fuzzy implication operators, Fuzzy Sets and Systems, 4, 13-30 (1980) · Zbl 0433.03013
[2] Bustince, H.; Burillo, P., Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 74, 237-244 (1995) · Zbl 0875.94156
[3] Bustince, H.; Burillo, P.; Soria, F., Automorphisms, negations and implication operators, Fuzzy Sets and Systems, 134, 209-229 (2003) · Zbl 1010.03017
[4] Bustince, H.; Mohedano, V.; Barrenechea, E.; Pagola, M., Definition and construction of fuzzy DI-subsethood measures, Information Sciences, 176, 3190-3231 (2006) · Zbl 1104.03052
[5] Chen, S. M., Measures of similarity between vague sets, Fuzzy Sets and Systems, 74, 217-223 (1995) · Zbl 0896.28010
[6] Chen, S. M.; Yeh, M. S.; Hsiao, P. Y., A comparison of similarity measures of fuzzy values, Fuzzy Sets and Systems, 72, 79-89 (1995)
[7] Chaira, T.; Ray, A. K., Fuzzy measures for color image retrieval, Fuzzy Sets and Systems, 150, 545-560 (2005) · Zbl 1065.68106
[8] Chaira, T.; Ray, A. K., Region extraction using fuzzy similarity measures, Journal of Fuzzy Mathematics, 11, 601-607 (2003) · Zbl 1098.68933
[9] Cheng, H. D.; Chen, C. H.; Chiu, H. H., Image segmentation using fuzzy homogeneity criterion, Information Sciences, 98, 237-262 (1997)
[10] Deluca, A.; Termini, S., A definition of a nonprobabilistic entropy in the setting of fuzzy set theory, Inform and Control, 20, 301-312 (1972) · Zbl 0239.94028
[11] De Meyer, H.; De Baets, B.; Janssens, S., Similarity measurement on leaf-labelled trees, (Proceedings of EUSFLAT 2001 (2001), De Montfort University Leicester: De Montfort University Leicester UK), 253-256
[12] Dubois, D.; Ostasiewicz, W.; Prade, H., Fuzzy sets: history and basic notions, (Dubois, D.; Prade, H., Fundamentals of Fuzzy Sets (2000), Kluwer: Kluwer Boston, MA), 21-124 · Zbl 0967.03047
[13] Dubois, D.; Prade, H., A unifying view of comparison indices in a fuzzy set-theoretic framework, (Yager, R. R., Recent Developments in Fuzzy Set and Possibility Theory (1982), Pergamon Press), 3-13
[14] Dumitrescu, D., Fuzzy correlation, Studia Universitatis Babes-Bolyai Mathematica, 23, 41-44 (1978) · Zbl 0377.94001
[15] Fan, J.; Xie, W., Some notes on similarity measure and proximity measure, Fuzzy Sets and Systems, 101, 403-412 (1999) · Zbl 0934.91009
[16] Fodor, J.; Roubens, M., Fuzzy preference modelling and multicriteria decision support, (Theory and Decision Library (1994), Kluwer Academic Publishers.) · Zbl 0827.90002
[17] T.M. Gale, N. Davey, K.R. Laws, M. Loomes, R.J. Frank, Self-organising map representations of greyscale images reflect human similarity judgements, in: Proceedings of the 2nd IEEE International Conference on Intelligent Systems, Varna, Bulgaria, 2004, pp. 66-70.; T.M. Gale, N. Davey, K.R. Laws, M. Loomes, R.J. Frank, Self-organising map representations of greyscale images reflect human similarity judgements, in: Proceedings of the 2nd IEEE International Conference on Intelligent Systems, Varna, Bulgaria, 2004, pp. 66-70.
[18] Gerstenkorn, T.; Manko, J., Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 44, 39-43 (1991) · Zbl 0742.04008
[19] Hillebrand, R.; Wang, P. P.; Gosele, U., A fuzzy logic approach to edge detection in HREM images of III-V crystals, Information Sciences, 93, 321-338 (1996)
[20] Hong, D. H., A note on correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 95, 113-117 (1998) · Zbl 0924.04002
[21] Hong, D. H.; Hwang, S. Y., Correlation of intuitionistic fuzzy sets in probability space, Fuzzy Sets and Systems, 75, 77-81 (1995) · Zbl 0854.60002
[22] Hong, D. H.; Kim, C., A note on similarity measures between vague sets and between elements, Information Sciences, 115, 83-96 (1999) · Zbl 0936.03052
[23] Jacard, P., Nouvelles recherches sur la distribution florate, Bulletin de la Societe Vaudoise des Sciences Naturelles, 44, 223-270 (1908)
[24] Klir, G. J.; Forlger, T. A., Fuzzy Sets: Uncertainty and Information (1988), Prentice-Hall International
[25] Klir, G.; Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications (1995), Prentice-Hall: Prentice-Hall Upper Saddle River, NJ · Zbl 0915.03001
[26] Liu, X., Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems, 52, 305-318 (1992) · Zbl 0782.94026
[27] Loia, V.; Sessa, S., Fuzzy relation equations for coding/decoding processes of images and videos, Information Sciences, 171, 145-172 (2005) · Zbl 1078.68815
[28] Lukac, R.; Smolka, B.; Martin, K.; Plataniotis, K. N.; Venetsanopoulos, A. N., Vector filtering for color imaging, IEEE Signal Processing Magazine, 22, 74-86 (2005)
[29] Montero, J., Rational aggregation rules, Fuzzy Sets and Systems, 62, 267-276 (1994) · Zbl 0828.90005
[30] Pappis, C. P.; Karacapilidis, N. I., A comparative assessment of measures of similarity of fuzzy values, Fuzzy Sets and Systems, 56, 171-174 (1993) · Zbl 0795.04007
[31] Prewitt, M. S., Object enhancement and extraction, (Rosenfeld, A.; Lipkin, B. S., Picture Processing and Psychophysics (1970), Academic Press: Academic Press New York), 75-149
[32] Santini, S.; Jain, R., Similarity measures, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 9, 1-13 (1999)
[33] Sinha, D.; Dougherty, E. R., Fuzzification of set inclusion: Theory and applications, Fuzzy Sets and Systems, 55, 15-42 (1993) · Zbl 0788.04007
[34] Smolka, B.; Lukac, R.; Chydzinski, A.; Plataniotis, K. N.; Wojciechowski, K., Fast adaptive similarity based impulsive noise reduction filter, Real-Time Imaging, 9, 261-276 (2003)
[35] Tizhoosh, H. R., Observer-dependent image enhancement, (Nachtegael, M.; Weken, D. V.; De Ville, D. V.; Kerre, E. E., Fuzzy Filters for Image Processing. Fuzzy Filters for Image Processing, Studies in Fuzziness and Soft Computing, vol. 122 (2003), Springer), 238-270
[36] E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica, III-1 (1979) 47-59 (in Spanish). English version reprinted in: S. Barro, A. Bugarn, A. Sobrino (Eds.), Advances in Fuzzy Logic, Universidad de Santiago de Compostela, 1998, pp. 31-43.; E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica, III-1 (1979) 47-59 (in Spanish). English version reprinted in: S. Barro, A. Bugarn, A. Sobrino (Eds.), Advances in Fuzzy Logic, Universidad de Santiago de Compostela, 1998, pp. 31-43.
[37] Twerski, A., Features of similarity, Psychology Review, 84, 327-352 (1977)
[38] Van der Weken, D.; Nachtegael, M.; Kerre, E. E., Using similarity measures and homogeneity for the comparison of images, Image and Vision Computing, 22, 695-702 (2004)
[39] Wang, W. J., New similarity measures on fuzzy sets and on elements, Fuzzy Sets and Systems, 85, 305-309 (1997) · Zbl 0904.04009
[40] Wang, X.; De Baets, B.; Kerre, E., A comparative study of similarity measures, Fuzzy Sets and Systems, 73, 259-268 (1995) · Zbl 0852.04011
[41] Wang, Y. H., Image indexing and similarity retrieval based on spatial relationship model, Information Sciences, 154, 39-58 (2003)
[42] Willmott, R., Two fuzzier implication operators in the theory of fuzzy power sets, Fuzzy Sets and Systems, 4, 31-36 (1980) · Zbl 0433.03014
[43] Young, V. R., Fuzzy subsethood, Fuzzy Sets and Systems, 77, 371-384 (1996) · Zbl 0872.94062
[44] Zwick, R.; Carlstein, E.; Budescu, D. V., Measures of similarity among fuzzy concepts: a comparative analysis, International Journal of Approximate Reasoning, 1, 221-242 (1987)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.