In multiple attribute decision analysis (MADA), one often needs to deal with both numerical data and qualitative information with uncertainty. It is essential to properly represent and use uncertain information to conduct rational decision analysis. Based on a multilevel evaluation framework, an evidential reasoning (ER) approach has been developed for supporting such decision analysis, the kernel of which is an ER algorithm developed on the basis of the framework and the evidence combination rule of the Dempster-Shafer (D-S) theory. The approach has been applied to engineering design selection, organizational self-assessment, safety and risk assessment, and supplier assessment. In this paper, the fundamental features of the ER approach are investigated. New schemes for weight normalization and basic probability assignments are proposed. The original ER approach is further developed to enhance the process of aggregating attributes with uncertainty. Utility intervals are proposed to describe the impact of ignorance on decision analysis. Several properties of the new ER approach are explored, which lay the theoretical foundation of the ER approach. A numerical example of a motorcycle evaluation problem is examined using the ER approach. Computation steps and analysis results are provided in order to demonstrate its implementation process.

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On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty

We study the reachability problem for systems implemented as feed-forward neural networks whose activation function is implemented via ReLU functions. We draw a correspondence between establishing whether some arbitrary output can ever be outputed by a neural system and linear problems characterising a neural system of interest. We present a methodology to solve cases of practical interest by means of a state-of-the-art linear programs solver. We evaluate the technique presented by discussing the experimental results obtained by analysing reachability properties for a number of benchmarks in the literature.

An approach to reachability analysis for feed-forward ReLU neural networks.

We provide a tutorial on the construction and evaluation of Markov decision processes (MDPs), which are powerful analytical tools used for sequential decision making under uncertainty that have been widely used in many industrial and manufacturing applications but are underutilized in medical decision making (MDM). We demonstrate the use of an MDP to solve as equential clinical treatment problem under uncertainty. Markov decision processes generalize standard Markov models in that a decision process is embedded in the model and multiple decisions are made over time. Furthermore, they have significant advantages over standard decision analysis. We compare MDPs to standard Markov-based simulation models by solving the problem of the optimal timing of living-donor liver transplantation using both methods. Both models result in the same optimal transplantation policy and the same total life expectancies for the same patient and living donor. The computation time for solving the MDP model is significantly smaller than that for solving the Markov model. We briefly describe the growing literature of MDPs applied to medical decisions. Key words: Markov decision processes; decision analysis; Markov processes. (Med Decis Making 2010;30:474–483)

http://homepages.cae.wisc.edu/~alagoz/MDM-MDP_tutorial.pdf

Markov Decision Processes: A Tool for Sequential Decision Making under Uncertainty:

Cyber-attack detection is used to identify cyber-attacks while they are acting on a computer and network system to compromise the security (e.g., availability, integrity, and confidentiality) of the system. This paper presents a cyber-attack detection technique through anomaly-detection, and discusses the robustness of the modeling technique employed. In this technique, a Markov-chain model represents a profile of computer-event transitions in a normal/usual operating condition of a computer and network system (a norm profile). The Markov-chain model of the norm profile is generated from historic data of the system's normal activities. The observed activities of the system are analyzed to infer the probability that the Markov-chain model of the norm profile supports the observed activities. The lower probability the observed activities receive from the Markov-chain model of the norm profile, the more likely the observed activities are anomalies resulting from cyber-attacks, and vice versa. This paper presents the learning and inference algorithms of this anomaly-detection technique based on the Markov-chain model of a norm profile, and examines its performance using the audit data of UNIX-based host machines with the Solaris operating system. The robustness of the Markov-chain model for cyber-attack detection is presented through discussions & applications. To apply the Markov-chain technique and other stochastic process techniques to model the sequential ordering of events, the quality of activity-data plays an important role in the performance of intrusion detection. The Markov-chain technique is not robust to noise in the data (the mixture level of normal activities and intrusive activities). The Markov-chain technique produces desirable performance only at a low noise level. This study also shows that the performance of the Markov-chain techniques is not always robust to the window size: as the window size increases, the amount of noise in the window also generally increases. Overall, this study provides some support for the idea that the Markov-chain technique might not be as robust as the other intrusion-detection methods such as the chi-square distance test technique , although it can produce better performance than the chi-square distance test technique when the noise level of the data is low, such as the Mill & Pascal data in this study.

Robustness of the Markov-chain model for cyber-attack detection

The Evidential Reasoning Approach for Multiple Attribute Decision Analysis Using Interval Belief Degrees

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Wayne L. Winston

Papers

Operations research: applications and algorithms / Wayne L. Winston