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Computing a T-transitive lower approximation or opening of a proximity relation

机译：计算T传递下级近似或接近关系的开度

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摘要

Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n~3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors' knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties.
机译：由于即使是那些接受其偏好中的可及性作为一致性条件的决策者也经常会侵犯可及性，因此处理不及物性偏好诱因的标准方法是寻找足够接近的可及性偏好关系，假定这种违反主要是由于决策者的估计误差。在某种程度上，引发的次数越多，不一致的可能性就越大。即使在备选方案或要分类的对象的数量相对较小的情况下，在模糊框架内多数情况也是如此。在本文中，我们提出了一种从反身和对称模糊关系计算T不可区分性的快速方法，该方法是任意左连续t范数为T。我们建议的计算近似值将采用O（n〜3）时间复杂度，其中n是要考虑的元素数，并有望产生T传递开口。据作者所知，没有其他提议的算法可以在保持反射性和对称性的同时计算T传递的较低近似值或开口。

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