Uncertainty analysis and sensitivity analysis should be important components of any analysis of a complex system, with (i) uncertainty analysis providing a representation of the uncertainty present in the estimates of analysis outcomes and (ii) sensitivity analysis identifying the contributions of individual analysis inputs to the uncertainty in analysis outcomes [1]. Probability theory provides the mathematical structure traditionally used in the representation of epistemic (i.e., state of knowledge) uncertainty, with the uncertainty in analysis outcomes represented with probability distributions and typically summarized as cumulative distribution functions (CDFs) or complementary cumulative distribution functions (CCDFs) [2], [3] and [4]. A variety of sensitivity analysis procedures have been developed for use in conjunction with probabilistic representations of uncertainty, including differential analysis [5] and [6], the Fourier amplitude sensitivity test (FAST) and related variance decomposition procedures [7], [8], [9], [10] and [11], regression-based techniques [12] and [13], and searches for nonrandom patterns [14]. Additional background information on uncertainty and sensitivity analysis is available in several review presentations [1], [14], [15], [16], [17], [18] and [19].
Although probabilistic representations of uncertainty have been successfully employed in many analyses, such representations have been criticized for inducing an appearance of more refined knowledge with respect to the existing uncertainty than is really present [20] and [21]. Much of this criticism derives from the use of uniform distributions to characterize uncertainty in the presence of little or no knowledge with respect to where the appropriate value to use for a parameter is located within a set of possible values [22, pp. 52–62]. As a result, a number of alternative mathematical structures for the representation of epistemic uncertainty have been proposed, including evidence theory, possibility theory, and fuzzy set theory [23], [24], [25] and [26].
Evidence theory provides a promising alternative to probability theory that allows for a fuller representation of the implications of uncertainty than is the case in a probabilistic representation of uncertainty [27], [28], [29], [30], [31], [32] and [33]. In particular, evidence theory involves two representations of the uncertainty associated with a set of possible analysis inputs or results: (i) a belief, which provides a measure of the extent to which the available information implies that the true value is contained in the set under consideration, and (ii) a plausibility, which provides a measure of the extent to which the available information implies that the true value might be contained in the set under consideration. One interpretation of the belief and plausibility associated with a set is that (i) the belief is the smallest possible probability for the set that is consistent with all available information and (ii) the plausibility is the largest possible probability for the set that is consistent with all available information. An alternative interpretation is that evidence theory is an internally consistent mathematical structure for the representation of uncertainty without any explicit conceptual link to probability theory. The mathematical operations associated with evidence theory are the same for both interpretations. Just as probability theory uses CDFs and CCDFs to summarize uncertainty, evidence theory uses cumulative belief functions (CBFs), cumulative plausibility functions (CPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative plausibility functions (CCPFs) to summarize uncertainty.
Although evidence theory is beginning to be used in the representation of uncertainty in applied analyses, the authors are unaware of any attempts to develop sensitivity analysis procedures for use in conjunction with evidence theory. Due to the importance of sensitivity analysis in any decision-aiding analysis, the potential usefulness of evidence theory will be enhanced if meaningful and practicable sensitivity analysis procedures are available for use in analyses that employ evidence theory in the representation of uncertainty. As a result, the focus of this presentation is on the development of sensitivity analysis procedures for use in conjunction with evidence theory representations of uncertainty.
After a brief overview of evidence theory (Section 2), the following topics are considered: (i) exploratory sensitivity analysis (Section 3), (ii) use of sensitivity analysis results in the stepwise construction of CCBFs and CCPFs (Section 4), (iii) summary sensitivity analysis of evidence theory representations of uncertainty (Section 5), (iv) example results (Section 6), (v) formal justification of procedure used in stepwise construction of CCBFs and CCPFs (Section 7), and (vi) concluding summary (Section 8).
