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About approximate inclusion and its axiomatization

机译：关于近似包含及其公理化

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This paper is devoted to an extension of the inclusion operator. The regular inclusion of A in B entails that any element of A is also a member of B. The idea suggested in this paper is to relax (or soften) the universal quantifier (all) into "almost all". It is shown that diverse approaches to the relaxation can be envisaged in order to design an approximate inclusion whose result is either Boolean, or valued in the unit interval. A set of axioms that was previously proposed for the characterization of graded inclusion of fuzzy sets is revisited in order to take into account the specificities of approximate inclusion. A concrete usage of this type of inclusion is illustrated in the area of databases, with the approximate division of fuzzy relations.
机译：本文致力于包含运算符的扩展。在B中常规包含A意味着A的任何元素也都是B的成员。本文提出的想法是将通用量词（全部）放宽（或软化）为“几乎全部”。结果表明，可以设想多种松弛方法，以设计一个近似包含，其结果为布尔值或在单位间隔内取值。为了考虑近似包含的特殊性，重新讨论了先前提出的用于表征模糊集合的分级包含的一组公理。在数据库区域中，通过模糊关系的近似划分，说明了这种包含类型的具体用法。

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