Contrast of a fuzzy relation

  • Authors:

  • H. Bustince;E. Barrenechea;J. Fernandez;M. Pagola;J. Montero;C. Guerra

  • Affiliations:

  • Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

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.