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Upper Bounding Overlaps by Groupings

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Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

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Abstract

This paper focuses on determining conditions to ensure that certain overlaps are less than or equal to certain groupings. We also show that the meaning of such conditions is connected with the use of overlaps and groupings in image processing. Hence we present some results that are connected with the mentioned goal and formulated by using the notions of f -bound overlap and f -bound grouping.

This work was supported by the European Regional Development Fund projects CZ.1.05/1.1.00/02.0070 and CZ.1.07/2.3.00/30.0010

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References

  1. Barrenechea, E., Bustince, H., De Baets, B., Lopez-Molina, C.: Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images. IEEE Transactions on Fuzzy Systems 19(5), 819–830 (2011)

    Article  Google Scholar 

  2. Bowyer, K., Kranenburg, C., Dougherty, S.: Edge detector evaluation using empirical roc curves. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, (xxiii+637+663), p. 2 (1999)

    Google Scholar 

  3. Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R.: Overlap functions. Nonlinear Analysis: Theory, Methods & Applications 72(3-4), 1488–1499 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bustince, H., Pagola, M., Mesiar, R., Hullermeier, E., Herrera, F.: Grouping, overlap, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Transactions on Fuzzy Systems 20(3), 405–415 (2012)

    Article  Google Scholar 

  5. Canny, J.: A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-8(6), 679–698 (1986)

    Article  Google Scholar 

  6. Dankova, M., Hodakova, P., Perfilieva, I., Vajgl, M.: Edge detection using f-transform. In: 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA), pp. 672–677 (November 2011)

    Google Scholar 

  7. Jurio, A., Bustince, H., Pagola, M., Pradera, A., Yager, R.: Some properties of overlap and grouping functions and their application to image thresholding. Fuzzy Sets and Systems (2013)

    Google Scholar 

  8. Melin, P., Mendoza, O., Castillo, O.: An improved method for edge detection based on interval type-2 fuzzy logic. Expert Systems with Applications 37(12), 8527–8535 (2010)

    Article  Google Scholar 

  9. Rosenfeld, A., Thurston, M.: Edge and curve detection for visual scene analysis. IEEE Transactions on Computers C-20(5), 562–569 (1971)

    Article  Google Scholar 

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Correspondence to Nicolás Madrid .

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Madrid, N., Barrenechea, E., Bustince, H., Fernadez, J., Perfilieva, I. (2013). Upper Bounding Overlaps by Groupings. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_35

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

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