Fuzzy Sets Over the Poset I
Authors : I. U. Tiryaki
Pages : 143-166
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Publication Date : 2008-02-01
Article Type : Research
Abstract :The author studies fuzzy sets over the poset I = [0, 1] with the usual order. These form a canonical example of fuzzy sets over a poset discussed in (Tiryaki, ˙I. 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.Keywords : Texture, Unit interval texture, Hutton algebra, Fuzzy subset, Soft fuzzy subset, Point, Copoint, Construct, SF-topology, Ditopology, Separation, Compactness, Generalized Lowen functor, Rotund soft fuzzy set, Lowen rotund functor, Preservation of topological properties