覆盖Value集

覆盖粗糙集和Vague集都是处理不确定性问题的数学工具,它们分别是粗糙集和模糊集的扩展。已有的覆盖粗糙集模型在求上、下近似时,可能将一些实际上并非肯定属于给定集合的元素纳入到下近似中,而一些可能属于给定集合的元素却没有纳入到上近似中,这就会改变一些元素与给定集合的关系。通过深入分析论域中的元素与其相关覆盖元之间的关系,建立了覆盖Vague集。该覆盖Vague集能够从一种新的角度反映出论域中各元素与给定集合之间的从属程度。进一步研究了覆盖Vague集与覆盖粗糙集中一些重要概念之间的关系。最后讨论了当覆盖退化为划分时覆盖Vague集的特性。

Covering Vague Sets

Both covering-based rough sets and vague sets are the mathematical tools to deal with the uncertainty information.The former is the extension of the rough set theory and the latter of the fuzzy sets.Computing the lower and the upper approximations with the existing covering-based rough set models,some elements,which are actually not sure whether they completely belong to the given set,may be put into the lower approximation.Similarly,some elements,which maybe belong to the given set,are excluded from the upper approximation.By analyzing carefully the relationship between the element of the universe and the covering-elements,a covering vague set was established.This covering vague set can reflect the degree of membership of every element of universe to the given set from a new viewpoint.Furthermore,some relationships between the covering vague set and some important concepts of covering-based rough sets were studied.Finally,the properties of a covering vague set that when a covering coincides with a partition were discussed.