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There are relatively few proposals for inconsistency measures for propositional belief bases. However inconsistency measures are potentially as important as information measures for artificial intelligence, and more generally for computer science. In particular, they can be useful to define various operators for belief revision, belief merging, and negotiation. The measures that have been proposed so far can be split into two classes. The first class of measures takes into account the number of formulae required to produce an inconsistency: the more formulae required to produce an inconsistency, the less inconsistent the base. The second class takes into account the proportion of the language that is affected by the inconsistency: the more propositional variables affected, the more inconsistent the base. Both approaches are sensible, but there is no proposal for combining them. We address this need in this paper: our proposal takes into account both the number of variables affected by the inconsistency and the distribution of the inconsistency among the formulae of the base. Our idea is to use existing inconsistency measures in order to define a game in coalitional form, and then to use the Shapley value to obtain an inconsistency measure that indicates the responsibility/contribution of each formula to the overall inconsistency in the base. This allows us to provide a more reliable image of the belief base and of the inconsistency in it.  相似文献
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It is well understood how to compute the average or centroid of a set of numeric values, as well as their variance. In this way we handle inconsistent measurements of the same property. We wish to solve the analogous problem on qualitative data: How to compute the “average” or consensus of a set of affirmations on a non-numeric fact, as reported for instance by different Web sites? What is the most likely truth among a set of inconsistent assertions about the same attribute?Given a set (a bag, in fact) of statements about a qualitative feature, this paper provides a method, based in the theory of confusion, to assess the most plausible value or “consensus” value. It is the most likely value to be true, given the information available. We also compute the inconsistency of the bag, which measures how far apart the testimonies in the bag are. All observers are equally credible, so differences arise from perception errors, due to the limited accuracy of the individual findings (the limited information extracted by the examination method from the observed reality).Our approach differs from classical logic, which considers a set of assertions to be either consistent (True, or 1) or inconsistent (False, or 0), and it does not use Fuzzy Logic.  相似文献
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