Outlier Detection under Interval and Fuzzy Uncertainty: Algorithmic Solvability and Computational Complexity

In many application areas, it is important to detect outliers. Traditional engineering approach to outlier detection is that we start with some “normal” values , compute the sample average , the sample standard variation , and then mark a value as an outlier if is outside the -sigma interval (for some pre-selected parameter ). In real life, we often have only interval ranges for the normal values . In this case, we only have intervals of possible values for the bounds and ! . We can therefore identify outliers as values that are outside all -sigma intervals. In this paper, we analyze the computational complexity of these outlier detection problems, and provide efficient algorithms that solve some of these problems (under reasonable conditions). We also provide algorithms that estimate the degree of “outlier-ness” of a given value – measured as the largest value for which is outside the corresponding " -sigma interval.