Exact Bounds for Interval and Fuzzy Functions Under Monotonicity Constraints, with Potential Applications to Biostratigraphy

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