r -蕴涵与交换原则:一个完整的表征

EUSFLAT Conf. Pub Date : 2011-08-06 DOI:10.2991/eusflat.2011.63

B. Jayaram, M. Baczyński, R. Mesiar

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引用次数: 5

摘要

众所周知，左连续T模T的残差It满足交换原理(EP)，即对于所有x,y,z∈[0,1]，It (x, It (y,z)) = It (y, It (x,z))。然而，正如文献中的许多例子所表明的那样，T的左连续性只是充分的，而不是必要的。本文研究了T范数T的残差满足(EP)的必要条件。本文给出了残差满足(EP)的t-模类的完整刻画。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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R-implications and the Exchange Principle: A Complete Characterization

It is well-known that the residual IT of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz., IT (x,IT (y,z)) = IT (y,IT (x,z)) for all x,y,z ∈ [0, 1]. However, the left-continuity of T is only sufficient and not necessary, as many examples in the literature illustrate. In this work we study the necessary conditions on a t-norm T for its residual to satisfy (EP). The work presents a complete characterization of the class of t-norms whose residuals satisfy (EP).

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EUSFLAT Conf.

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