Bustince, H. and Barrenechea, E. and Fernández, J. and Pagola, M. and Montero, Javier and Guerra, C. (2010) Contrast of a fuzzy relation. Information Sciences, 180 (8). pp. 1326-1344. ISSN 0020-0255
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In this paper we address a key problem in many fields: how a structured data set can be analyzed in order to take into account the neighborhood of each individual datum. We propose representing the dataset as a fuzzy relation, associating a membership degree with each element of the relation. We then introduce the concept of interval-contrast, a means of aggregating information contained in the immediate neighborhood of each element of the fuzzy relation. The interval-contrast measures the range of membership degrees present in each neighborhood. We use interval-contrasts to define the necessary properties of a contrast measure, construct several different local contrast and total contrast measures that satisfy these properties, and compare our expressions to other definitions of contrast appearing in the literature. Our theoretical results can be applied to several different fields.
In an Appendix A, we apply our contrast expressions to photographic images.
|Uncontrolled Keywords:||Fuzzy relation; Interval-contrast; Local contrast; Total contrast|
|Subjects:||Sciences > Computer science > Artificial intelligence|
M. Adel, D. Zuwala, M. Rasigni, S. Bourennane, Filtering noise on mammographic phantom images using local contrast modification functions, Image Vis. Comput. 26 (2008) 1219–1229.
A. Amo, J. Montero, E. Molina, Representation of consistent recursive rules, Euro. J. Oper. Res. 130 (2001) 29–53.
M. Baczyn´ ski, B. Jayaram, Fuzzy Implications (Studies in Fuzziness and Soft Computing), Springer, Berlin, 2008.
E. Barrenechea, H. Bustince, M. Pagola, J. Fernandez, Construction of interval-valued fuzzy entropy invariant by translations and scalings, Soft Comput., in press. doi:10.1007/s00500-009-0480-7.
G. Beliakov, A. Pradera, T. Calvo, Aggregation Functions: A Guide for Practitioners (Studies In Fuzziness and Soft Computing), vol. 221, Springer, 2007, pp. 1–37.
P. Burillo, H. Bustince, Entropy on intutionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets Syst. 78 (1996) 305–316.
H. Bustince, Construction of intutionistic fuzzy relations with predetermined properties, Fuzzy Sets Syst. 109 (2000) 379–403.
H. Bustince, P. Burillo, F. Soria, Automorphisms, negations and implication operators, Fuzzy Sets Syst. 134 (2003) 209–229.
H. Bustince, P. Burillo, Mathematical analysis of interval-valued fuzzy relations: application to approximate reasoning, Fuzzy Sets Syst. 113 (2000) 205–219.
H. Bustince, P. Burillo, Structures on intutionistic fuzzy relations, Fuzzy Sets Syst. 78 (1996) 293–303.
H. Bustince, E. Barrenechea, M. Pagola, R. Orduna, Construction of interval type 2 fuzzy images to represent images in grayscale: false edges, in: Proceedings of the IEEE International Conference on Fuzzy Systems, London, July 23–26, 2007, pp. 73–78.
H. Bustince, J. Montero, M. Pagola, E. Barrenechea, D. Gómez, A survey of interval-valued fuzzy sets, in: W. Pedrycz, A. Skowron, V. Kreinovich (Eds.), Handbook of Granular Computing, Wiley, New Jersey, 2008.
H. Bustince, M. Pagola, E. Barrenechea, Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images, Inform. Sci. 177 (2007) 906–929.
H. Bustince, V. Mohedano, E. Barrenechea, M. Pagola, Definition and construction of fuzzy DI-subsethood measures, Inform. Sci. 176 (2006) 3190–3231.
H. Bustince, E. Barrenechea, M. Pagola, Generation of interval-valued fuzzy and Atanassov’s intuitionistic fuzzy connectives from fuzzy connectives and from Ka operators: laws for conjunctions and disjunctions, amplitude, Int. J. Intell. Syst. 23 (6) (2008) 680–714.
H. Bustince, E. Barrenechea, M. Pagola, J. Fernandez, Interval-valued fuzzy sets constructed from matrices: application to edge detection, Fuzzy Sets Syst. 160 (13) (2009) 1819–1840.
H. Bustince, J. Montero, E. Barrenechea, M. Pagola, Semiautoduality in a restricted family of aggregation operators, Fuzzy Sets Syst. 158 (12) (2007) 1360–1377.
T. Calvo, A. Kolesarova, M. Komornikova, R. Mesiar, Aggregation operators: properties, classes and construction methods, in: T. Calvo, G. Mayor, R. Mesiar (Eds.), Aggregation Operators New Trends and Applications, Physica-Verlag, Heidelberg, 2002, pp. 3–104.
Y.F. Chen, Y.K. Chan, C.C. Huang, et al, A multiple-level visual secret-sharing scheme without image size expansion, Inform. Sci. 177 (2007) 4696–4710.
H.D. Cheng, C.H. Chen, Image segmentation using fuzzy homogeneity criterion, Inform. Sci. 98 (1997) 237–262.
H.D. Cheng, H. Xu, A novel fuzzy logic approach to mammogram contrast enhancement, Inform. Sci. 148 (2002) 177–184.
H.D. Cheng, M. Xue, X.J. Shi, Contrast enhancement based on a novel homogeneity measurement, Pattern Recognition 36 (2003) 2687–2697.
V. Cutello, J. Montero, Recursive connective rules, Int. J. Intell. Syst. 14 (1999) 3–20.
G. Deschrijver, E.E. Kerre, On the composition of intuitionistic fuzzy relations, Fuzzy Sets Syst. 136 (2003) 333–361.
G. Deschrijver, C. Cornelis, E.E. Kerre, On the representation of intuitionistic fuzzy T-norms and T-conorms, IEEE Trans. Fuzzy Syst. 12 (1) (2004) 45–61.
D. Dubois, W. Ostasiewicz, H. Prade, Fuzzy sets: history and basic notions, in: D. Dubois, H. Prade (Eds.), Fundamentals of Fuzzy Sets, Kluwer, Boston, MA, 2000, pp. 21–124.
M. Friedman, M. Schneider, A. Kandel, The use of Weighted fuzzy expected value (WFEV) in fuzzy expert systems, Fuzzy Sets Syst. 31 (1989) 37–45.
J. Fodor, M. Roubens, Fuzzy preference modelling and multicriteria decision support, in: Theory and Decision Library, Kluwer Academic Publishers, 1994.
R.C. Gonzalez, R.E. Woods, Digital image processing, in: Theory and Decision Library, third ed., Prentice-Hall, 2008.
O. Ibáñez, L. Ballerini, O. Cordón, S. Damas, J. Santamara, An experimental study on the applicability of evolutionary algorithms to craniofacial superimposition in forensic identification, Inform. Sci. 179 (2009) 3998–4028.
M.Z. Jahromi, E. Parvinnia, R. John, A method of learning weighted similarity function to improve the performance of nearest neighbor, Inform. Sci. 179 (17) (2009) 2964–2973.
S. Jenei, A more efficient method for defining fuzzy connectives, Fuzzy Sets Syst. 90 (1997) 25–35.
A.R. Jimenez-Sanchez, J.D. Mendiola-Santibanez, I.R. Terol-Villalobos, G. Herrera-Ruiz, D. Vargas-Vazquez, J.J. Garcia-Escalante, A. Lara-Guevara, Morphological background detection and enhancement of images with poor lighting, IEEE Trans. Image Process. 18 (3) (2009) 613–623.
A. Kandel, W.J. Byatt, Fuzzy sets fuzzy algebra and fuzzy statistics, Proc. IEEE 66 (1978) 1619–1639.
G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, Upper Saddle River, NJ, 1995.
M. Mas, M. Monserrat, J. Torrens, E. Trillas, A survey on fuzzy implication functions, IEEE Trans. Fuzzy Syst. 15 (6) (2007) 1107–1121.
S.C. Matz, R.J.P. de Figueiredo, A nonlinear image contrast sharpening approach based on Munsell’s scale, IEEE Trans. Image Process. 15 (2006) 900–909.
W.H. Mcilhagga, K.T. Mullen, Contour integration with colour and luminance contrast, Vis. Res. 9 (1996) 1265–1279.
J.M. Mendel, Advances in type-2 fuzzy sets and systems, Inform. Sci. 177 (2007) 84–110.
J.M. Mendel, R.I. John, F. Liu, Interval type-2 fuzzy logic systems made simple, IEEE Trans. Fuzzy Syst. 14 (2006) 808–821.
A. Michelson, Studies in Optics, University of Chicago Press, 1927.
M. Mizumoto, K. Tanaka, Some properties of fuzzy sets of type 2, Inform. Control 31 (1976) 312–340.
J. Montero, D. Gómez, H. Bustince, On the relevance of some families of fuzzy sets, Fuzzy Sets Syst. 158 (2007) 2429–2442.
S.K. Pal, N.R. Pal, Segmentation using contrast and homogeneity measures, Pattern Recognition Lett. 5 (1987) 293–304.
E. Peli, Contrast in complex images, J. Opt. Soc. Am. A 7 (10) (1990) 2032–2040.
A. Polesel, G. Ramponi, V.J. Mathews, Image enhancement via adaptive unsharp masking, IEEE Trans. Image Process. 9 (3) (2000) 505–510.
R. Sambuc, Function U-Flous, Application a l’aide au diagnostic en pathologie thyroidienne, These de Doctorat en Medicine, Marseille, 1975.
P. Smets, P. Magrez, Implication in fuzzy logic, Int. J. Approx. Reason. 1 (1987) 327–347.
H.R. Tizhoosh, Observer–dependent image enhancement, in: M. Nachtegael, D. van der Weken, D. van De Ville, E.E. Kerre (Eds.), Fuzzy Filters for Image Processing, Springer, Germany, 2003, pp. 238–270.
E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica, III-1 (1979) 47-59, (in Spanish). Reprinted (English version) in: Advances of Fuzzy Logic (Eds. S. Barro et altri-Universidad de Santiago de Compostela (1998), pp. 31–43.
I.B. Turksen, Type 2 representation and reasoning for computing with words, Fuzzy Sets Syst. 127 (2002) 17–36.
D. Van der Weken, M. Nachtegael, E. Kerre, Combining neighbourhood-based and histogram similarity measures for the design of image quality measures, Image Vis. Comput. 25 (2007) 184–195.
|Deposited On:||19 Jul 2012 09:20|
|Last Modified:||19 Apr 2016 14:14|
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