The aim of the paper is to highlight the challenges in making decisions when there is incomplete evidence and information. By understanding the challenges, businesses should be able to make faster, higher quality, decisions. This paper proposes methodologies incorporating probabilistic and other knowledge management techniques to assist in decision making under these conditions. A wide variety of models are generally used to help in the decision making process. With reference to the parameters and structure of a model, four basic types can be identified depending on the degrees of vagueness and completeness.

Type 1 models are deterministic and characteristic of much hard science and engineering. Type 2 models allow for inputs known only as distributions. These models are probabilistic and the basis of probabilistic reserves assessment, probabilistic risk analysis and many economic models. Type 3 models are characterised by vagueness in the overall structure and with input parameters expressible only as ranges and limits. Techniques such as imprecise probabilities (fuzzy logic's and Interval Probability Theory) have recently been developed to handle these models. Type 4 models are characteristic of many complex situations where actions in the future and / or issues of relevance and completeness are central. In other contexts such problems have been referred to as "messy" or "wicked". Many of the problems concerning project evaluations are Type 3 and Type 4, as are most problems that include elements of human judgement, interpretation and choice.

We describe a methodology and mathematics to address Type 3 & 4 problems based on hierarchical process modelling, recording of attributes and a calculus that combines incomplete evidence. We discuss the modelling, philosophy and mathematics that allows explicit incorporation of vagueness and incompleteness. Our approach is illustrated through case studies, including gas to liquid (GTL) investment decisions, prospect evaluation and carbon dioxide sequestration options.

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