# Application of interval-valued fuzzy integration to evaluate computer attacks

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## Abstract

It is difficult for a network administrator to prevent or defend all kinds of computer and network attacks with limited time and resources. Being able to compare attacks based on subjective preferences is a natural way to identify the most critical attacks. ^ In order to compare attacks, we need to describe each attack with respect to a set of well defined criteria or attributes. By studying the potential impacts of common computer attacks, we define the set of criteria to compare attacks. ^ We consider comparing attacks as a multicriteria decision making (MCDM) problem. An approach to solve this problem is the so-called utility theory approach where we try to find a function u : X → R such that x is preferred to y (or more harmful in our particular case) if and only if u( x) is larger than u(y), where X is the set of possible attacks. So the problem reduces to identifying a utility function that agrees with a decision maker's partial preferences. ^ A very natural and simple choice for the utility function is a weighted sum (or an additive function). But this approach suffers a serious drawback as an additive approach is only valid when the attributes are independent. Therefore, we use non-additive approaches instead. ^ In MCDM, fuzzy (or non-additive) integrals with respect to fuzzy measures can be used as an aggregation operator on monodimensional utility functions. However, the definition of fuzzy measures needs an exponential number of parameters, with respect to the number of criteria. ^ In order to reduce the cost, we use 2-additive measures which are a particular type of fuzzy measures. This limits the complexity to O( n2) and this approach works even if the attributes are not independent. ^ We combine Choquet integral with interval values which is an accurate yet tractable way to solve MCDM problems, in particular to compare computer attacks. ^

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