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Fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces

机译：L-Convex空间框架中船体运营商和间隔运算符的模糊对手

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摘要

For fuzzy counterparts of hull operators and interval operators, two types of fuzzy hull operators and one type of fuzzy interval operators are proposed. Firstly, the concept of L-hull operators is introduced and the resulting category is shown to be isomorphic to that of L-convex spaces. Secondly, considering the graded inclusions of L-subsets, the notion of L-ordered hull operators is presented, which is shown to be categorically isomorphic to strong L-convex structures. Finally, the concept of L-interval operators is introduced and it is shown that there is a Galois correspondence between the category of L-interval spaces and that of L-convex spaces. In particular, the category of arity 2 L-convex spaces can be reflectively embedded into that of L-interval spaces. (C) 2018 Elsevier B.V. All rights reserved.
机译：对于船体操作员和间隔操作员的模糊对手，提出了两种类型的模糊船体操作员和一种类型的模糊间隔操作员。首先，引入了L-HULL运算符的概念，并且结果类别被显示为L-Convex空间的同性。其次，考虑到L-亚群的分级夹杂物，提出了L订购的船体运算符的概念，其被示出为对强L-凸结构的分类构态。最后，介绍了L-间隔操作员的概念，并显示了L-凸空间的L型间隔空间和L-凸空间的类别之间存在Galois对应关系。特别地，ARIITE 2 L-凸起空间的类别可以反射地嵌入到L-间隔空间的范围内。 （c）2018年elestvier b.v.保留所有权利。

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