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The minimal mathematical structure for a synchronic approach to fuzzy set theory

机译:模糊集理论的同步方法的最小数学结构

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The paper gives a concrete presentation of the minimal structure on the monoid of an external subset classifier of a universe of usual sets with Zadeh-Goguen L-fuzzy subsets. The result was first investigated by the first author, with the aim of providing a new insight into the synchronic approach to fuzzy set theory. The extensive use of conceptual mathematics (i.e. category theory) in the original paper, restricts the audience of readers of this analysis to persons who are already acquainted with conceptual mathematics. The aim of this paper is to avoid as much as possible the use of functorial terminology in the presentation of the minimal mathematical structure on the set of truth values, for a synchronic approach to fuzzy sets. By doing so, we hope to widen the audience of scientists interested in the foundation of Zadeh-Goguen L-fuzzy sets and to provide a new way of looking at the synchronic approach to fuzziness.
机译:本文给出了带有Zadeh-Goguen L-fuzzy子集的一组通常集的外部子集分类器的类上的最小结构的具体表示。第一作者首先对结果进行了研究,目的是为模糊集理论的同步方法提供新的见解。原始论文中概念数学(即类别理论)的广泛使用将本分析读者的受众限制在已经熟悉概念数学的人员中。本文的目的是在对真值集进行同步处理时,尽可能避免使用函子术语来表示真值集的最小数学结构。通过这样做,我们希望扩大对Zadeh-Goguen L模糊集的建立感兴趣的科学家的受众,并提供一种新的方法来研究模糊性的同步方法。

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