Fuzzy sets and sheaves. Part Ⅰ Basic concepts

Ulrich Hoehle

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Fuzzy sets and sheaves. Part Ⅰ Basic concepts

机译：模糊集和滑轮。第一部分基本概念

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This essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory, respectively, of the theory of complete Ω-valued sets. Hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect. Part Ⅰ of this essay divided into a series of two papers presents such basic concepts as Ω-valued equalities, espaces etales, singleton monad, the change of base and the subobject classifier axiom. The application of these tools to the sheaf-theoretic foundations of fuzzy sets will appear in Part Ⅱ.

机译：本文表明，模糊集理论的大部分实际上分别是完整Ω值集理论的Sheaf理论的子领域。因此，模糊集理论比许多人期望的更接近于数学的主流。本文的第一部分分为两篇论文，介绍了Ω值等式，espaces etales，单例monad，基数的变化和子对象分类器公理等基本概念。这些工具在模糊集的层理论基础上的应用将在第二部分中介绍。

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来源
《Fuzzy sets and systems》 |2007年第11期|p.1143-1174|共32页
作者
Ulrich Hoehle;
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作者单位

Fachbereich C Mathematik und Naturwissenschaften Bergische Universitaet, D-42097 Wuppertal, Germany;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类模糊数学;
关键词
category theory; Ω-valued sets; espace etale; singleton monad; complete Ω-valued sets; membership functions; geometric morphisms;

机译：范畴论;Ω值集;空间传说;单子单子集;完整Ω值集;隶属函数;几何同态;

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1. Fuzzy sets and sheaves. Part Ⅱ: Sheaf-theoretic foundations of fuzzy set theory with applications to algebra and topology [J] . Ulrich Hoehle Fuzzy sets and systems . 2007,第11期

机译：模糊集和滑轮。第二部分：模糊集理论的Sheaf理论基础及其在代数和拓扑中的应用
2. Mathematics in the Context of Fuzzy Sets: Basic Ideas, Concepts, and Some Remarks on the History and Recent Trends of Development [J] . Alexander Å ostaksab* Mathematical Modelling and Analysis . 2011,第2期

机译：模糊集上下文中的数学：基本思想，概念和关于发展历史和近期趋势的一些评论
3. MODELING OF COGNITIVE STRUCTURE OF UNCERTAIN SCIENTIFIC CONCEPTS USING FUZZY-ROUGH SETS AND INTUITIONISTIC FUZZY SETS: EXAMPLE OF THE LIFE CONCEPT [J] . NURETTIN YOREK, SERKAN NARLI International journal of uncertainty, fuzziness and knowledge-based systems . 2009,第5期

机译：基于模糊粗糙集和直觉模糊集的不确定科学概念的认知结构建模：生命概念的例子
4. Comparison of the concepts of soft set, fuzzy soft set and L-fuzzy set [C] . Fu Li, Wang Pingshu 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery . 2011

机译：软集，模糊软集和L-模糊集的概念比较
5. A hill-climbing algorithm combined with fuzzy set concepts toward the development of a compact associative classifier. [D] . Mitra, Soumyaroop. 2008

机译：结合模糊集概念的爬山算法，用于开发紧凑型关联分类器。
6. m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets [O] . Juanjuan Chen, Shenggang Li, Shengquan Ma, -1

机译：m-极模糊集：双极模糊集的扩展
7. Basics on Random Sets and Random Fuzzy Sets [O] . Fumio HIAI 1998

机译：随机集和随机模糊集的基础知识
8. Fuzzy Sets as Random Level Sets: Implications and Extensions of the Basic Results [R] . Goodman, I. R. 1991

机译：模糊集作为随机水平集：基本结果的含义和扩展

Fuzzy sets and sheaves. Part Ⅰ Basic concepts

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