Minimality and comparison of sets of multi-attribute vectors

In a decision-making problem, there can be uncertainty regarding the user preferences. We assume a parameterised utility model, where in each scenario we have a utility function over alternatives, and where each scenario represents a possible user preference model consistent with the input preference information. With a set A of alternatives available to the decision maker, we can consider the associated utility function, expressing, for each scenario, the maximum utility among the alternatives. We consider two main problems: firstly, finding a minimal subset of A that is equivalent to it, i.e., that has the same utility function. Secondly, we consider how to compare A to another set of alternatives B, where A and B correspond to different initial decision choices. We derive mathematical results that allow different computational techniques for these two problems, using linear programming, and especially, using the extreme points of the epigraph of the utility function

Onshore Cross Country Pipelines Risk Assessment and Decision Making Under Uncertainty

Onshore cross-country pipelines are a critical component of refined product transportation in the oil and gas industry. The integrity of those pipelines is key to maintaining supply security, protecting the environment and human life. However, due to incessant pipeline damages and resultant consequences of fires, explosion and environmental pollution because of third-party events in Nigeria, stakeholders are looking at solutions to reduce the human, environmental and the financial losses. The main objective of this research is to develop risk-based models for identifying and assessing the oil and gas pipelines failures, including risk reduction decision-making framework and cost-benefit estimates. One of the major challenges of carrying out a pipeline risk assessment in some regions is the lack of reliable and objective data for data-driven analysis. The models developed in this thesis addressed this shortcoming and allowed the subjective data to be incorporated into the analysis. Hazards identification and ranking of the failure modes have been carried out using a modified FMEA based Fuzzy Rules Base (FRB) and Grey Relations Theory (GRT) to accommodate the uncertainty in terms of inadequate data. The results of modified approach serve as an input to developing the failure likelihood and this involves a Bayesian Network (BN) model of the identified failure mode. The BN model has been developed using Hugin software. The results of the BN feeds into the Evidential Reasoning (ER) model to aid risk management decision-making. Also, cost benefit estimates have been carried out to assess the cost benefit of implementing any risk reduction options. All the objectives set out in the thesis have been achieved. The research has contributed to the stated challenges by identifying the parameters for high failure incidences and develop various models and assess contributing failure factors and the risk control options to reducing the likelihood of the failure including cost benefit estimates