A fuzzy version of Tarski’s fixpoint theorem. (English) Zbl 1108.06008

The author establishes a fuzzy set version of Tarski’s classical fixed-point theorem in a complete lattice. In particular, the following statement is proved:
Let \((X, r)\) be a nonempty \(r\)-fuzzy complete lattice and let \(f\: X \rightarrow X\) be a \(r\)-fuzzy monotone map. Then the set \(\text{Fix}(f)\) of all fixed points of \(f\) is a nonempty \(r\)-fuzzy complete lattice.
Definitions of all concepts appearing in the above theorem can be found in the reviewed paper.


06D72 Fuzzy lattices (soft algebras) and related topics
06B23 Complete lattices, completions
54H25 Fixed-point and coincidence theorems (topological aspects)
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