Fuzzy Sets Over the Poset I

Authors : İ. U. TİRYAKİ

Pages : 143-166

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Publication Date : 2008-02-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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