Componentwise decomposition of some lattice-valued fuzzy integrals

  • Authors:

  • Adrian Ban;Ioan Fechete

  • Affiliations:

  • Department of Mathematics and Informatics, University of Oradea, Universitatii 1, 410087 Oradea, Romania;Department of Mathematics and Informatics, University of Oradea, Universitatii 1, 410087 Oradea, Romania

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

Lattice-valued fuzzy measures are lattice-valued set functions which assign the bottom element of the lattice to the empty set, the top element of the lattice to the entire universe and satisfy the property of monotonicity. If the lattice is complete then a lattice-valued fuzzy integral of Sugeno type, with similar properties such as the Sugeno integral in its original form, can be introduced in a natural way. The main result of the paper is a componentwise decomposition theorem of an L-valued fuzzy integral to its L-valued fuzzy integrals components, where L is a complete lattice with negation and L={(@a,@b);@a,@b@?L,@a=