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Extensions of fuzzy relational compositions based on generalized quantifiers

机译：基于广义量词的模糊关系合成的扩展

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The aim of this paper is to extend the fuzzy relational compositions motivated by their applications to medical diagnosis problem by Bandler and Kohout. These compositions employ two quantifiers, the universal quantifier and the existential quantifier. As there exists a big gap between these two quantifiers, that may be appropriately filled in by intermediate generalized quantifiers, we take this as a motivation for our study. In particular, we introduce the concept of fuzzy relational compositions based on generalized quantifiers. Furthermore, we show that the properties that are typically valid for standard fuzzy relational compositions are also valid for the compositions based on generalized quantifiers, yet sometimes in a weaken form. Apart from fuzzy relational compositions, the use of generalized quantifiers is also applied to images and preimages of fuzzy sets under fuzzy relations. (C) 2017 Elsevier B.V. All rights reserved.
机译：本文的目的是将Bandler和Kohout提出的模糊关系组合应用于医学诊断问题。这些组合使用两个量词，即通用量词和存在量词。由于这两个量词之间存在较大的差距，中间的广义量词可以适当地弥补这一差距，因此我们以此为动机。特别是，我们介绍了基于广义量词的模糊关系合成的概念。此外，我们表明通常对标准模糊关系合成有效的属性对于基于广义量词的合成也有效，但有时呈弱化形式。除模糊关系合成外，广义量词的使用也适用于模糊关系下的模糊集的图像和原像。 （C）2017 Elsevier B.V.保留所有权利。

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