An Interval Metric
Roque Mendes Prado Trindade, Benjamín Bedregal, Adrião Duarte Dória Neto, Benedito Melo · InTech eBooks · 2010
By it was said above the distance notion is ubiquitous to mainly research areas and for system modelling with uncertainties. The usual metrics fail to accomplish those necessities, because it is not indeed an interval metric. By other hand the proposed metric is not only a generalisation of the usual Euclidean metric but also it is an essentially interval metric, as it is was shown above. With the proposed metric one can redefine the notions of limit, continuity, neighbourhood, convergence etc. Most basic properties of mathematics can be redefined with the proposed notion of distance. The proposed metric accomplishes the numeric aspect if one takes an interval as an approximation of a real number and the logic aspects if one takes an interval as a fuzzy information.