The Topological Modification of the L-fuzzy Unit Interval
The Topological Modification of the L-fuzzy Unit Interval
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DOI：
10.1007/978-94-011-2616-8_12
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
T. Kubiak
中科院分区：
文献类型：
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作者：
T. Kubiak
1975 年，Hutton 发明了 L-模糊单位区间 I(L)，这是一个非常富有成效的概念，使他能够根据 Urysohn 类型引理来描述正常的 L-模糊拓扑空间，并为 L-模糊空间引入一个非常有效的完整正则公理（参见 [Hutton 1975 1977]）。尽管 I(L) 作为一个空间在模糊拓扑中的适用性与实数单位区间在一般拓扑中的作用相同，已被许多其他作者证明（例如 [Liu 1983]、[Liu and Luo 1989]、[Rodabaugh 1983b, 1988a]、[Kubiak 1987, 1986]），但这种规范的 L-模糊的结构空间尚未被充分理解。 [Rodabaugh 1982a] 对截至 1982 年为止获得的 L-模糊单位区间结果进行了调查。然而，该论文包含的开放性问题多于结果。
In 1975, Hutton invented the L-fuzzy unit intervalI(L)a very fruitful concept which enabled him to characterize the normal L-fuzzy topological spaces in terms of Urysohn’s type lemma and to introduce a very efficient complete regularity axiom for L-fuzzy spaces (see [Hutton 1975 1977]). Although the appropriateness ofI(L)as a space which plays the same role in fuzzy topology as the real unit interval plays in general topology, has been proved by a number of other authors (e.g. [Liu 1983], [Liu and Luo 1989], [Rodabaugh 1983b, 1988a], [Kubiak 1987, 1986]), the structure of this canonical L-fuzzy space is not yet well-understood. A survey of the results on the L-fuzzy unit interval that have been obtained up to 1982 was made by [Rodabaugh 1982a]. That paper, however, contains more open questions than results.