Review of Uncertainty Reasoning Approaches as Guidance for Maritime and Offshore Safety-Based Assessment

Many different formal techniques have been developed over the past two decades for dealing with uncertain information for decision making. In this paper we review some of the most important ones, i.e., Bayesian theory of probability, Dempster-Shafer theory of evidence, and fuzzy set theory, describe how they work and in what ways they differ from one another, and show their strength and weakness respectively as well as their connection. We also consider hybrid approaches which combine two or more approximate reasoning techniques within a single reasoning framework. These have been proposed to address limitations in the use of individual techniques. The study is intended to provide guidance in the process of developing frameworks for safety-based decision analysis using different methods for reasoning under uncertainty. 1. Uncertainty in Decision Making In conventional information processing techniques it is often assumed that problems are well structured, complete information is always available and information processing procedures can be clearly defined. However, in many realworld decision making problems, this is not always the case and decisions making is often associated with uncertainty. “Uncertainty” is a context dependent concept. There does not exist a comprehensive and unique definition of uncertainty. One definition of uncertainty is given as follows [Zimmermann 2000]: “Uncertainty is a situation in which a person does not have the quantitatively and qualitatively appropriate information to describe, prescribe or predict deterministically and numerically a system, its behavior or other characteristics.” This definition focuses on the human related, subjective interpretation, which depends on the quantity and quality of information about a system that is available to a human observer. Uncertainty has many different sources and different types. A review of the literature shows a variety of treatments of uncertainty. Uncertainty can be broadly classified into three types, namely randomness, fuzziness and incompleteness [Blockley and Godfrey 2001]. Uncertainty can be attributed to vagueness where there are ill-defined boundaries and ambiguity and where there are several choices for a given situation [Klir and Yuan 1995, Ibrahim and Ayyub 1992]. Uncertainties can be classified into two broad categories, namely probabilistic and cognitive [Gupta 1992]. They can also be referred to as epistemic and aleatory uncertainties, respectively [Pate’-Cornell 1996, Bonissone and Tong 1985, Kanal and Lemmer 1986, Krause and Clark 1993, Stefik 1995, Zimmermann 2000]. It was suggested in [Zimmermann 2000] that only a careful analysis of the contextual features of uncertainty will lead to the selection of the most suitable uncertainty theory. Methods for dealing with uncertainty in many areas of artificial intelligence (AI) have received considerable attention for more than a decade. Several numerical and symbolic methods have been proposed for handling uncertain information [Clark 1990, Ibrahim and Ayyub 1992, Kruse et al. 1992, Krause and Clark 1993]. Three of the most common methods of representing and reasoning with uncertain knowledge are Bayesian probability theory [Pearl 1988], Dempster-Shafer theory of evidence [Dempster 1968 and 1969, Shafer 1976], and fuzzy set theory [Zadeh 1965]. 2. Bayesian Theory of Probability The classical approach to address uncertainty is the Bayesian theory of probability. Probability theory has been used to model precisely described, repetitive experiments with observable but uncertain outcomes. In this approach, uncertain variables are assumed to be described by statistical parameters which define the probability of the variable having a ∗ The corresponding author: [email protected]