Fixed points for fuzzy mappings

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In this paper the problem of the existence and computation of fixed points for fuzzy mappings is approached. A fuzzy mapping R over a set X is defined to be a function attaching to each x in X a fuzzy subset Rχ of X. An element x of X is called fixed point of R iff its membership degree to Rχ is at least equal to the membership degree to Rχ of any y ε{lunate} X, i.e. Rχ(χ)≥ Rχ(y)(∀y ε{lunate} X). Two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described. The convergence theorem of our algorithm is proved under the restrictive assumption that for any x in X, the membership function of Rχ has a 'complementary function'. Examples of fuzzy mappings having this property are given, but the problem of proving general criteria for a function to have a complementary remain open.

Original languageEnglish
Pages (from-to)191-207
Number of pages17
JournalFuzzy Sets and Systems
Issue number2
StatePublished - Mar 1982
Externally publishedYes


  • Eaves' fixed point algorithm
  • Fixed point
  • Fuzzy mapping
  • Fuzzy sets
  • Kuhn's fixed point algorithm
  • Linear function relative to a triangulation
  • Triangulation

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence


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