Extension of a class of decomposable measures using fuzzy pseudometrics

Dong Qiu; Weiquan Zhang; Cheng Li

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Extension of a class of decomposable measures using fuzzy pseudometrics

机译：使用模糊伪度量扩展一类可分解测度

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摘要

In this paper, we consider a topological approach to extension of t-conorm-based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets. We prove that every non-strict continuous Archimedean t-conorm-based decomposable measure can be extended from an algebra to the completion of this algebra under the fuzzy pseudometric and then to the sigma-algebra generated by this algebra. The existence of such an extension follows very simply from the well-known Carathe'odory result. However, our topological proof offers an intuitive interpretation of the extension of decomposable measures.

机译：在本文中，我们通过在集合的代数上引入模糊伪度量结构，考虑了一种拓宽基于t-conorm的可分解度量的拓扑方法。我们证明，每一个基于非严格连续的基于阿基米德t-conorm的可分解测度都可以从代数扩展到在模糊伪度量下该代数的完成，然后再扩展到由该代数生成的sigma-代数。这种扩展的存在非常简单地从众所周知的“卡拉特”气味结果中得出。但是，我们的拓扑证明可以直观地解释可分解度量的扩展。

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来源
《Fuzzy sets and systems》 |2013年第1期|33-44|共12页
作者
Dong Qiu; Weiquan Zhang; Cheng Li;
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作者单位

College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, PR China;

School of Information Engineering, Guangdong Medical College, Dongguan, Guangdong 523808, PR China;

School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China;

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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
non-additive measures; decomposable measures; fuzzy metric; space; t-norm; t-conorm;

机译：非累加措施;可分解的措施;模糊度量空间;t范数康康;

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1. Pseudometric Generating Property of Fuzzy Measures Convergence in Fuzzy Measure [J] . Li Jun Journal of Southeast University . 2000,第2期

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2. Extension on the fuzzy integral based on⊕-decomposable measure [J] . MamadouTraore International journal of mathematics and mathematical sciences . 2001,第8期

机译：基于⊕可分解测度的模糊积分扩展
3. Pseudometric generating property and autoconitnutiy of fuzzy measures [J] . Qingshan Jiang, Shengrui Wang, Djemel Ziou Fuzzy sets and systems . 2000,第2期

机译：伪测量的生成性质和模糊度量的自相关性
4. On some extensions for S-decomposable fuzzy measures [C] . Torra, V. Fuzzy Systems, 2001. The 10th IEEE International Conference on . 2001

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5. Using Fuzzy Inference in Psychophysical Detection Experiments to Separate Hits, False Positives and Guesses; And Using Wavelet Decomposition to Detect Periodic Signals in Head Accelerometry Measures; Both in Posturally Perturbed Standing Subjects. [D] . Sani, Shahrokh Norouzi. 2014

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7. Extension on the fuzzy integral based on ⊕-decomposable measure [O] . Mamadou Traore 2001

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8. Extension of the Measure-Free Approach to Conditioning of Fuzzy Sets and Other Logics. (Reannouncement with New Availability Information). [R] . Goodman, I. R., Stein, D. W. 1989

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Extension of a class of decomposable measures using fuzzy pseudometrics

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