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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.

MSC:

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