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Tensor products of complete lattices and their application in constructing quantales

机译：完整格的张量积及其在构造量子中的应用

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This paper aims to implement tensor products of complete lattices into fuzzy set theory. The most convenient approach for this purpose is to view the tensor product of two complete lattices as the family of all join reversing maps between those lattices. We show that some fundamental constructions in fuzzy set theory are tensor products. Examples of such circumstances include the following (to mention only three of them): the complete lattice of all lower semicontinuous maps from a topological space into a continuous lattice is the tensor product of the topology of the space and the range lattice; a binary operation coming from Zadeh's extension principle is the tensor product of the Minkowski multiplication with the multiplication of the underlying unital quantale; triangle functions on nonnegative left-continuous distribution functions are tensor products of the real unit interval and the extended nonnegative half-line equipped, respectively, with a left-continuous t-norm and the usual addition. (C) 2016 Elsevier B.V. All rights reserved.
机译：本文旨在将完整格的张量积实现为模糊集理论。为此目的，最方便的方法是将两个完整晶格的张量积视为这些晶格之间所有联接反转图的族。我们证明了模糊集理论中的一些基本构造是张量积。这种情况的示例包括以下内容（仅提及其中的三个）：从拓扑空间到连续晶格的所有下半连续映射的完整晶格是空间拓扑和范围晶格的张量积； Zadeh的扩展原理产生的二进制运算是Minkowski乘积与基础单位量子乘积的张量积。非负左连续分布函数上的三角函数分别是实数单元区间和扩展的非负半线的张量积，分别装备有左连续t范数和通常的加法。 （C）2016 Elsevier B.V.保留所有权利。

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