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[References: 40 tit.]

It is proposed in the paper the interval data fusion procedure intended for determination of an interval to be consistent with maximal number of given initial intervals (not necessary consistent among each other) and to be with maximal likelihood including a value x* that can serve as representative of all the given intervals. An algorithm of the interval fusion with preference aggregation (IF&PA) is proposed and discussed that can be carried out with help of representation of intervals on the real line by weak order relations (or rankings) over a set of discrete values belonging to these intervals. It is possible to determine a consensus ranking for collection of discrete values rankings, corresponding to initial intervals. The highest ranked value, accepted as a result of the fusion, guarantees improved accuracy and robustness of the interval data fusion procedure outputs. It is considered a space of weak orders induced by the intervals, its properties and dimension. A reasonable number choice problem of discrete values, representing the interval data, is investigated. Related to the problem, computing experiment results and recommendations are given. The interval data fusion procedures can be widely applied in interlaboratory comparisons, prediction of fundamental constant values on the base of different measured values, conformity testing, enhancement of multisensor readings accuracy in sensor networks, etc.