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Applications of Graph Theory
Published in Rowan Garnier, John Taylor, Discrete Mathematics, 2020
In chapter 10 we used the analogy of a road map to illustrate various graph-theoretic concepts. There is one aspect of a road map, however, which is not modelled by a graph—namely, the distances between towns. In many applications of graph theory it is important to be able to attach numbers to the edges of the graph which represent certain physical quantities. For example, if we wish to use a graph to represent an electrical network, it may be important to record the resistances of each of the components represented by the edges of the graph. Similarly, if our graph is a mathematical model of a network of fluid-carrying pipes, we might wish to include information about the capacities of the various different pipes on the graph itself. In probability and decision theory, trees are used where the edges represent possible outcomes of an experiment or possible decisions to be made. It is often useful to assign probabilities to the outcomes which are represented by the corresponding edges.
Risk Assesment
Published in Srinivasan Chandrasekaran, Offshore Structural Engineering, 2017
Decision trees are applied within the framework of decision theory, which is also one of the basic frameworks of risk assessment. This is due to the fact that risk analysis serves the purpose of decision-making and reliability which is more toward engineering judgment. Followed by the detailed risk analysis, one has to plan for risk mitigation or risk reduction, if the risk is beyond the predefined acceptable level. It is very important to note that risk level in the offshore industry should be predefined as per international practice and also needs to be declared in the public domain for approval from a competent authority. Therefore, either to act on the risk assessment results or not is a decision-making process or therefore decision trees are very much part of risk assessment. Decision analysis is the framework for risk assessment and risk evaluation as well. Figure 4.10 shows a typical decision tree used in risk assessment.
Supplier Networks
Published in Vivek Kale, Agile Network Businesses, 2017
Decision theory provides a normative framework for decision making during uncertainty. It is based on the concept of rationality—that is, that an agent should try to maximize its utility or minimize its costs. This assumes that there is some way to assign utilities (usually a number that can correspond to monetary value or any other scale) to the result of each alternative action, such that the best decision is the one that has the highest utility. In general, an agent is not sure about the results of each of its possible decisions, so it needs to take this into account when it estimates the value of each alternative. In decision theory, we consider the expected utility, which takes an average of all the possible results of a decision, weighted by their probability. Thus, in a nutshell, a rational agent must select the decision that maximizes its expected utility.
Toward a Standard of Medical Care: Why Medical Professionals Can Refuse to Prescribe Puberty Blockers
Published in The New Bioethics, 2023
But RATIONAL REFUSAL requires an account of rationality, to which I now turn. Intuitively, a choice is rational only when it is directed at bringing about the desired effect. When providing a standard of medical care, the clinician should not, I have argued, induce dysfunctional conditions. However, that some service not detract from proper functioning is not the only requirement for medical rationality; the probability of inducing dysfunctional conditions matters for rational decision making. Recently, contemporary decision theory has embodied this balance between the quality of an outcome and the probability that some action will bring about that outcome through expected utility formulas. As a result, I will use basic tenants of decision theory to determine whether or not an action can be considered medically rational. In causal decision theory, an action is rational if and only if it maximizes expected utility given the causal decision theoretic formula for expected utility: where is the utility value assigned to the agent’s performing some action, A, and some state, Si, coming about and is the probability assignment given by the agent that A causes Si to come about (Weirich 2020). The basic idea is that one is rational to select an option, given a set of choices, if and only if that option has the greatest expected utility.
DECAS: a modern data-driven decision theory for big data and analytics
Published in Journal of Decision Systems, 2021
Nada Elgendy, Ahmed Elragal, Tero Päivärinta
Decision theory, simply put, is the study of choices in order to make a decision. However, decisions are far from simple, and their surrounding theories have been complex subjects of focus and debate throughout many decades of interdisciplinary research (Hansson, 1994). Moreover, decision theory has primarily focused on rational decision making (Peterson, 2011). It is a systematic study of the goal-directed, non-random behaviours and actions of decision makers, under events or conditions when different options or courses of action can be chosen (Hansson, 1994). Hence, the decision problem is the situation in which a decision maker chooses what to do from a set of alternative acts, which are affected by events taking place outside of the decision maker’s control, and accordingly result in various outcomes with positive or negative payoffs (Peterson, 2011). Accordingly, decision theory usually focuses on the outcome of decisions as judged by pre-determined criteria or on means-ends rationality (Hansson, 2011).
Optimal maintenance plan for two-level assembly system and risk study of machine failure
Published in International Journal of Production Research, 2019
Zouhour Guiras, Sadok Turki, Nidhal Rezg, Alexandre Dolgui
Decision theory proposes a set of mathematical tools that help decision-making in a random and risky environment and guide decision-makers in their choice. In the literature, many researchers are interested in risk issues, and they have tried to classify types and propose tools to cope with some risks that can lead to bad consequences. Our goal is to evaluate risk following an adopted strategy or a decision taken. In recent work, Guiras et al. (2018a) tried to help decision-makers, under certain conditions, found the optimal plan of disassembly/assembly system as well as to adapt to the potential risk du to failure machine that can disturb the supply chain, which has an impact on the calculated profit. Indeed, In Guiras et al. (2018b), they proposed analytical models to quantify the risk of lost profit stem from product returns and the integration of an imperfect maintenance policy.