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Keywords:
fuzzy relation; reflexivity; symmetry; connectedness; $\star $-transitivity; transitivity; weak property; relation aggregation; mean; arithmetic mean; quasi-arithmetic mean; quasilinear mean; weighted average
fuzzy relation; reflexivity; symmetry; connectedness; $\star $-transitivity; transitivity; weak property; relation aggregation; mean; arithmetic mean; quasi-arithmetic mean; quasilinear mean; weighted average
Summary:
We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special table at the end of the paper.
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