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Dilation and Erosion of Spatial Bipolar Fuzzy Sets

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Applications of Fuzzy Sets Theory (WILF 2007)

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Abstract

Bipolarity has not been much exploited in the spatial domain yet, although it has many features to manage imprecise and incomplete information that could be interesting in this domain. This paper is a first step to address this issue, and we propose to define mathematical morphology operations on bipolar fuzzy sets (or equivalently interval valued fuzzy sets or intuitionistic fuzzy sets).

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References

  1. Dubois, D., Kaci, S., Prade, H.: Bipolarity in Reasoning and Decision, an Introduction. In: International Conference on Information Processing and Management of Uncertainty, IPMU 2004, Perugia, Italy, pp. 959–966 (2004)

    Google Scholar 

  2. Cacioppo, J.T., Gardner, W.L., Berntson, G.G.: Beyond Bipolar Conceptualization and Measures: The Case of Attitudes and Evaluative Space. Personality and Social Psychology Review 1, 3–25 (1997)

    Article  Google Scholar 

  3. Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Information Sciences 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  5. Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminology Difficulties in Fuzzy Set Theory – The Case of Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 156, 485–491 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bustince, H., Burillo, P.: Vague Sets are Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 79, 403–405 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bloch, I.: Fuzzy Relative Position between Objects in Image Processing: a Morphological Approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 657–664 (1999)

    Article  Google Scholar 

  8. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)

    MATH  Google Scholar 

  9. Atanassov, K.T., Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade’s papers, H.: Terminology Difficulties in Fuzzy Set Theory – The Case of Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 156, 496–499 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cornelis, C., Kerre, E.: Inclusion Measures in Intuitionistic Fuzzy Sets. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 345–356. Springer, Heidelberg (2003)

    Google Scholar 

  11. Heijmans, H.J.A.M., Ronse, C.: The Algebraic Basis of Mathematical Morphology – Part I: Dilations and Erosions. Computer Vision, Graphics and Image Processing 50, 245–295 (1990)

    Article  MATH  Google Scholar 

  12. Bloch, I., Maître, H.: Fuzzy Mathematical Morphologies: A Comparative Study. Pattern Recognition 28, 1341–1387 (1995)

    Article  MathSciNet  Google Scholar 

  13. Sinha, D., Dougherty, E.R.: Fuzzification of Set Inclusion: Theory and Applications. Fuzzy Sets and Systems 55, 15–42 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. de Baets, B.: Fuzzy Morphology: a Logical Approach. In: Ayyub, B., Gupta, M. (eds.) Uncertainty in Engineering and Sciences: Fuzzy Logic, Statistics and Neural Network Approach, pp. 53–67. Kluwer Academic, Boston, MA (1997)

    Google Scholar 

  15. Nachtegael, M., Kerre, E.E.: Classical and Fuzzy Approaches towards Mathematical Morphology. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing. Studies in Fuzziness and Soft Computing, pp. 3–57. Physica-Verlag, Springer, Heidelberg (2000)

    Google Scholar 

  16. Deng, T.Q., Heijmans, H.: Grey-Scale Morphology Based on Fuzzy Logic. Journal of Mathematical Imaging and Vision 16, 155–171 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Deschrijver, G., Cornelis, C., Kerre, E.: On the Representation of Intuitionistic Fuzzy t-Norms and t-Conorms. IEEE Transactions on Fuzzy Systems 12, 45–61 (2004)

    Article  Google Scholar 

  18. Cornelis, C., Deschrijver, G., Kerre, E.: Implication in Intuitionistic Fuzzy and Interval-Valued Fuzzy Set Theory: Construction, Classification, Application. International Journal of Approximate Reasoning 35, 55–95 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Bloch, I.: Duality vs Adjunction and General Form for Fuzzy Mathematical Morphology. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 354–361. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Francesco Masulli Sushmita Mitra Gabriella Pasi

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Bloch, I. (2007). Dilation and Erosion of Spatial Bipolar Fuzzy Sets. In: Masulli, F., Mitra, S., Pasi, G. (eds) Applications of Fuzzy Sets Theory. WILF 2007. Lecture Notes in Computer Science(), vol 4578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73400-0_49

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  • DOI: https://doi.org/10.1007/978-3-540-73400-0_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73399-7

  • Online ISBN: 978-3-540-73400-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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