In many problems in science and engineering ranging from astrophysics to geosciences to financial analysis, we know that a physical quantity y depends on the physical quantity x, i.e., y = (x) for some function (x), and we want to check whether this dependence is monotonic. Specifically, finitely many measurements of xi and yi = (xi) have been made, and we want to check whether the results of these measurements are consistent with the monotonicity of (x). An efficient parallelizable algorithm is known for solving this problem when the values xi are known precisely, while the values yi are known with interval uncertainty. In this paper, we extend this algorithm to a more general (and more realistic) situation when both xi and yi are known with interval uncertainty.
Abstract-The age of fossil species in samples recovered from a well that penetrates an undisturbed sequence of sedimentary rocks increases with depth. The results of biostratigraphic analysis of such a sequence consist of several age-depth values -both known with interval (or fuzzy) uncertainty -and we would like to find, for each possible depth, the interval of the possible values of the corresponding age. A similar problem of bounding an intervally (fuzzily) defined function under monotonicity constraint occurs in many other application areas. In this paper, we provide an efficient algorithm for solving this problem.
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