A Survey of Outlier Detection Methods in Network Anomaly Identification <s> Definition 5: RMF (rough membership function)- <s> Rough set theory, introduced by Zdzislaw Pawlak in the early 1980s [11, 12], is a new mathematical tool to deal with vagueness and uncertainty. This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition. <s> BIB001 </s> A Survey of Outlier Detection Methods in Network Anomaly Identification <s> Definition 5: RMF (rough membership function)- <s> “One person's noise is another person's signal” (Knorr and Ng 1998). In recent years, much attention has been given to the problem of outlier detection, whose aim is to detect outliers—objects who behave in an unexpected way or have abnormal properties. Detecting such outliers is important for many applications such as criminal activities in electronic commerce, computer intrusion attacks, terrorist threats, agricultural pest infestations. In this paper, we suggest to exploit the framework of rough sets for detecting outliers. We propose a novel definition of outliers—RMF (rough membership function)-based outliers, by virtue of the notion of rough membership function in rough set theory. An algorithm to find such outliers is also given. And the effectiveness of RMF-based method is demonstrated on two publicly available data sets. <s> BIB002
based outliers BIB001 BIB002 . A RMF is defined as follows. Let IS=(U, A, V, f ) be an information system, X ⊆ U and X = Φ. U is a non-empty finite set of objects, A a set of attributes, V the union of attribute domains, and f : U × A → V a function such that for any X ∈ U and a ∈ A, f (x, a) ∈ V a . Let ν be a given threshold value. For any x ∈ X, if ROF X (x) > ν, x is called a rough membership f unction (RM F )-based outlier with respect to X in IS, where ROF X (x) is the rough outlier factor of x with respect to X in IS. The rough outlier f actor is defined as The RMF is µ where 