Titlebook: Computing Statistics under Interval and Fuzzy Uncertainty; Applications to Comp Hung T. Nguyen,Vladik Kreinovich,Gang Xiang Book 20121st ed

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Towards a Formalization of Digital Forensics . . .: .. In many practical applications, we need to estimate the sample variance . = . · ., where . = . · . ..

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Computing under Interval Uncertainty: When Measurement Errors Are Small: . .. When the measurement errors Δ. are relatively small, we can use a simplification called .. The main idea of linearization is as follows.

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Computing under Interval Uncertainty: Computational ComplexityIn this chapter, we will briefly describe the computational complexity of the range estimation problem under interval uncertainty.. .. Let us start with the simplest case of a linear function. = .(.,..., .) = . + . .· ...In this case, substituting the (approximate) measured values ., we get the approximate value. = . + . .· .for ..

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Computing Variance under Interval Uncertainty: An Example of an NP-Hard Problem . . .: .. In many practical applications, we need to estimate the sample variance . = . · ., where . = . · . ..

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Computing under Fuzzy Uncertainty Can Be Reduced to Computing under Interval Uncertaintyrst reformulate fuzzy techniques in an interval-related form..In some situations, an expert knows exactly which values of . are possible and which are not. In this situation, the expert’s knowledge can be naturally represented by describing the set of all possible values.

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Computing under Interval Uncertainty: General Algorithmssome applications, it is important to guarantee that the (unknown) actual value . of a certain quantity does not exceed a certain threshold .0. The only way to guarantee this is to have an interval . = [., . ] which is guaranteed to contain . (i.e., for which . ? . ) and for which . ≤ .0.