Fuzzy sets over the poset $Bbb{I}$

The author studies fuzzy sets over the poset $Bbb {I}$ = [0, 1] with the usual order. These form a canonical example of fuzzy sets over a poset dis- cussed in (Tiryaki, İ.U. and Brown, L.M. Plain textures and fuzzy sets via posets, preprint). Characterizations of these so called “soft fuzzy sets” are obtained, and soft fuzzy sets are shown to have a richer mathematical theory than classical I-fuzzy sets. In particular soft fuzzy points behave like the points of crisp set theory with respect to join, and moreover there exists a Lowen type functor from Top to the construct SF-Top that preserves both separation and compactness.

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