# An Intuitionistic Fuzzy-Rough Set-Based Classification for Anomaly Detection
## 1 Introduction
In [31], the authors proposed an approach called density-increasing path (DIP) to address issues of arbitrary shapes and unknown cluster numbers appearing during clustering processes. Most of the aforesaid methods only addressed the accuracy of the anomaly detection and a few addressed the false positive rates of the methods. Since the increase in the false positive rate decreases the detection rates and thus the efficacy of any classifier, it is required to minimize the false positive rates. Again, the normal and anomalous behaviors of the system are difficult to predict as there is no precise boundary differentiating one from another. In this scenario, either fuzzy set theory or rough set theory, or the combination of both, can effectively be utilized. [PERSON] [32] introduced fuzziness in the realm of mathematics by formally defining it as a generalization of ordinary set. [PERSON] [33] introduced intuitionistic fuzzy sets (IFSs) by generalizing them in terms of membership and nonmembership functions. Most of the works on anomaly detection used [PERSON]'s [32] fuzzy set, and a few only used IFS. Since the IFS has the inherent ability to tackle the imbalance and overlapping data [34], it can efficiently be used to describe the uncertainty, imprecision, and vagueness in more generalized ways than the traditional fuzzy approaches [32]. Considering the strength of the intuitionistic fuzzy sets, in [35], the authors proposed an intuitionistic approach to detect anomaly from time series data. In [36], the authors proposed the formula for correlation coefficient of intuitionistic fuzzy sets whose value lies in the interval [0, 1]. Fuzzy relation, \(\alpha\)-cut of a fuzzy relation, and fuzzy equivalence relations were introduced in [37; 38]. [PERSON] [39] introduced the rough set theory to deal with uncertainty, imprecision, or vagueness that exist in the datasets. Using the features of an equivalence relation, [40] nicely applied the rough-set-based classification to discrete datasets. In [41], the authors proposed an efficient method using fuzzy neighborhood rough set for the detection anomaly in large datasets. In [42], the authors proposed an efficient fuzzy-rough-set-based algorithm for feature selection. In [43; 44], the authors proposed two density-based approaches using neutrosophic sets and fuzzy proximity relations for the detection anomaly. In [45], the authors proposed an NN classification algorithm which uses the fuzzy-rough lower and upper approximations to classify test objects, or to predict their decision value. The methods discussed above used the parameters such as entropy and weighted density as classification criterion for anomaly detection. However, when using correlation coefficient of intuitionistic fuzzy sets, classification rules can be generated where each data instance participating in the rules is characterized by its membership as well as non-membership values defined over a universe of discourse. [PERSON] et al. [46] introduced nano topological space with respect to a subset \(X\) of universe \(U\) in terms of lower and upper approximation of \(X\). In [47], the authors not only introduced a nano topology structure but also applied it in medical diagnosis. In [48], the authors introduced three novel fuzzy nano topologies. Most classification-based anomaly detection algorithms developed up until today used different well-known measures to differentiate classes, and very few works were reported using the statistical measures such as correlation coefficient. Secondly, most of the fuzzy-rough approaches consider the corresponding fuzziness in Zadeh's sense [32]. However, if the approach can be extended to the intuitionistic fuzzy set, then the detected anomalies can provide more information about the system. In this article, a hybrid approach consisting of intuitionistic fuzzy set (IFS) and rough set (RS) was used in the classification algorithm for the anomaly detection of network datasets. The objectives of the paper are threefold.