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The rapid increase in the number of malicious programs has made malware forensics a daunting task and caused users’ systems to become in danger. Timely identification of malware characteristics including its origin and the malware sample family would significantly limit the potential damage of malware. This is a more profound risk in Cyber-Physical Systems (CPSs), where a malware attack may cause significant physical damage to the infrastructure. Due to limited on-device available memory and processing power in CPS devices, most of the efforts for protecting CPS networks are focused on the edge layer, where the majority of security mechanisms are deployed. Since the majority of advanced and sophisticated malware programs are combining features from different families, these malicious programs are not similar enough to any existing malware family and easily evade binary classifier detection. Therefore, in this article, we propose a novel multilabel fuzzy clustering system for malware attack attribution. Our system is deployed on the edge layer to provide insight into applicable malware threats to the CPS network. We leverage static analysis by utilizing Opcode frequencies as the feature space to classify malware families. We observed that a multilabel classifier does not classify a part of samples. We named this problem the instance coverage problem. To overcome this problem, we developed an ensemble-based multilabel fuzzy classification method to suggest the relevance of a malware instance to the stricken families. This classifier identified samples of VirusShare, RansomwareTracker, and BIG2015 with an accuracy of 94.66%, 94.26%, and 97.56%, respectively.

In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan-Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown MorganVoyce coefficients. Thereby, the solution is obtained in terms of Morgan-Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures.

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