L-fuzzy quantifiers of type determined by fuzzy measures

  • Authors:
  • Antonín Dvořák;Michal Holčapek

  • Affiliations:
  • Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic;Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2009

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Abstract

The aim of this paper is, first, to introduce two new types of fuzzy integrals, namely, @?-fuzzy integral and --fuzzy integral. The first integral is based on a fuzzy measure of L-fuzzy sets and the second one on a complementary fuzzy measure of L-fuzzy sets, where L is a complete residuated lattice. Some of their properties and a relation to the fuzzy (Sugeno) integral are investigated. Second, using these integrals, two classes of monadic L-fuzzy quantifiers of type are defined. These L-fuzzy quantifiers can be used for modeling the semantics of natural language quantifiers like ''all'', ''some'', ''many'', ''none'', ''at most half'', etc. Several semantic properties of these L-fuzzy quantifiers are studied.