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Arnold et el, Thanks for your comments. I have extracted the definition with related proofs for the committee to review. Please see the attachment. Relational operations are very fundamental in real arithmetic. The committee may want to consider it in interval arithmetic. Best regards, Chenyi >>> Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> 11/19/2008 8:02 AM >>> Chenyi Hu schrieb: > In addition to Boolean valued operations, interval relational operations <, <=, >, >= are useful in decision making. Since intervals are not comparable in binary logic, we have developed fuzzy order relations for intervals to deal with interval valued matrix game and interval weighted graph. I would suggest the committee to consider include fuzzy order relational operations. The problem with fuzzy operators is that there are too many different versions possible, and none is distinguished by strong theoretical properties, since a clear semantics for fuzzy sets is missing. I propose to leave fuzzy stuff out. > References can be found in our recent book "Knowledge Processing with Interval and Soft Computing" (Springer, 2008) pp. 149-152 and 168-172. Please provide an online summary if you want to keep your suggestion alive. Arnold Neumaier
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intervalFuzzyRelation.pdf
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