Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Computing variance for interval data is NP-hard
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Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds Δ on the measurement errors. In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. As a result, we often have bounds with excess width. In this paper, we show that one way to remedy this problem is to extend interval technique to rough-set computations, where at each stage, in addition to intervals of possible values of the quantities, we also keep rough sets representing possible values of pairs (triples, etc.). The paper's outline is as follows: we formulate the main problem (Section 1), briefly overview interval computations techniques solve this problem (Section 2), and then explain how the main ideas behind interval computation techniques can be extended to computations with rough sets (Section 3).