## 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)

### Keywords:

fuzzy set; fuzzy order relation; complete lattices
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