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首页> 外文期刊>Fuzzy sets and systems >A graded approach to cardinal theory of finite fuzzy sets, part Ⅱ: Fuzzy cardinality measures and their relationship to graded equipollence
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A graded approach to cardinal theory of finite fuzzy sets, part Ⅱ: Fuzzy cardinality measures and their relationship to graded equipollence

机译：有限模糊集基本理论的一种分级方法，第二部分：模糊基数测度及其与分级等价性的关系

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In this article, we propose an axiomatic system for fuzzy "cardinality" measures (referred to as fuzzy c-measures for short) assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains. The system generalizes an axiomatic system introduced by J. Casasnovas and J. Torrens (2003). We show that each fuzzy c-measure is determined by two appropriate homomorphisms between the reducts of residuated-dually residuated (rdr-)lattices. For linearly ordered rdr-lattices, we prove that each fuzzy c-measure is a product of a non-decreasing and a non-increasing fuzzy c-measure, which indicates that there is a close relation between fuzzy c-measures and FGCount, FLCount and FECount provided by L.A. Zadeh (1983) and generalized by M. Wygralak (2001). Finally, the relationship of fuzzy c-measures to graded equipollence introduced in the first part of this contribution is analyzed. (C) 2018 Elsevier B.V. All rights reserved.
机译：在本文中，我们提出了一种用于模糊“基数”测度（简称为模糊c测度）的公理系统，为每个有限模糊集分配一个表示该模糊集包含的元素数量的广义基数。该系统概括了J. Casasnovas和J. Torrens（2003）引入的公理系统。我们表明，每个模糊c量度由残差-正常残差（rdr-）格的还原之间的两个适当的同态确定。对于线性有序rdr晶格，我们证明每个模糊c量度都是非递减和非递增模糊c量度的乘积，这表明模糊c量度与FGCount，FLCount有密切关系由LA Zadeh（1983）提供并由M. Wygralak（2001）推广的FECount。最后，分析了该贡献的第一部分中引入的模糊c测度与等值的等价关系。 （C）2018 Elsevier B.V.保留所有权利。

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