An improved representation theorem of L-fuzzy sets

Lingxian Meng; Xuzhu Wang; Etienne Kerre

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An improved representation theorem of L-fuzzy sets

机译：L-模糊集的改进表示定理

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摘要

In this paper we present an extension of the famous representation theorem of Negoita and Ralescu. In this theorem the authors proved that the structure of lattice-valued fuzzy sets is dual isomorphic to the structure of lattice-valued flou sets for a special kind of lattices satisfying an additional condition that resembles the characterization of a supremum in chains. In this paper we show that this condition can be dropped and replaced by adding an antitone involution to both structures.

机译：在本文中，我们提出了Negoita和Ralescu的著名表示定理的扩展。在该定理中，作者证明格值模糊集的结构与特殊条件下满足特殊条件的特殊格的格值flou集的结构是双重同构的，该条件类似于链上极值的表征。在本文中，我们表明可以通过向两个结构添加反色调对合来消除和替换此条件。

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来源
《Fuzzy sets and systems》 |2010年第24期|p.3141-3147|共7页
作者
Lingxian Meng; Xuzhu Wang; Etienne Kerre;
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作者单位

Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, PR China;

rnDepartment of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, PR China;

Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium;

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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
关键词
l-fuzzy set; isomorphism; representation theorem;

机译：模糊集同构表示定理;

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An improved representation theorem of L-fuzzy sets

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