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Extending fuzzy logics with many hedges

机译：用许多树篱扩展模糊逻辑

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Fuzzy logic aims at modeling logical reasoning with vague or imprecise statements, which may contain linguistic hedges. In fact, many hedges, e.g., very, highly, rather, and slightly, can be used simultaneously to express different levels of emphasis. Moreover, each hedge might have a dual one, e.g., slightly can be seen as a dual hedge of very. Thus, it is necessary to extend systems of fuzzy logic with multiple hedges. This work proposes two axiomatizations for multiple hedges as an expansion of a core fuzzy logic. In one axiomatization, hedges do not have any dual one while in the other, each hedge can have its own dual one. It is shown that the proposed logics not only cover a large class of hedge functions but also have all completeness properties as the underlying logic w.r.t. the class of their chains as well as distinguished subclasses of their chains, including standard completeness. The axiomatizations are also extended to the first-order level. Furthermore, we present a method to build linguistic fuzzy logics based on the axiomatizations and a hedge algebra, whose corresponding algebras use a linguistic truth domain taken from the hedge algebra, for representing and reasoning with linguistically-expressed human knowledge, where truth values of vague sentences are given in linguistic terms. (C) 2018 Elsevier B.V. All rights reserved.
机译：模糊逻辑旨​​在用模糊或不精确的陈述来建模逻辑推理，其中可能包含语言对冲。实际上，许多树篱，例如非常，高度，相当和轻微的树篱，可同时用于表达不同程度的强调。而且，每个套期保值可能具有双重套期保值，例如，可以将其视为非常的双重套期保值。因此，有必要扩展具有多个树篱的模糊逻辑系统。这项工作提出了两个针对多个树篱的公理化，作为核心模糊逻辑的扩展。在一个公理化中，树篱没有任何双重对偶，而在另一个树篱中，每个树篱都可以有自己的双重对偶。结果表明，所提出的逻辑不仅涵盖了一大类对冲函数，而且还具有作为基础逻辑的所有完整性属性。链的类别以及链的杰出子类别，包括标准完整性。公理化也扩展到一阶水平。此外，我们提出了一种基于公理化和对冲代数的语言模糊逻辑的构建方法，对冲代数的对应代数使用取自对冲代数的语言真域，用语言表达的人类知识来表示和推理，其中模糊的真值句子以语言表达。 （C）2018 Elsevier B.V.保留所有权利。

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