Qualitative capacities: Basic notions and potential applications

A Qualitative Counterpart of Belief Functions with Application to Uncertainty Propagation in Safety Cases

“…In contrast, we outline the qualitative approach in [3][4][5]. Let L be a finite totally ordered set representing certainty levels.…”

“…This is more general than possibility theory where the case (1, 1) is not allowed. Figure 1 presents the credibility and information orderings on pairs (belief, disbelief) including extreme cases [5]. A proposition A is at least as credible as B if γ(A) ≥ γ(B) and γ(¬A) ≤ γ(¬B) (solid arrows from B to A), thus ranging from certainty of falsity (0, 1) up to certainty of truth (1, 0).…”

“…The scale L has the same number of elements as K (i.e., 3 here). The mapping f : D × K → L × L: must satisfy some conditions [5]:…”

“…Indeed, qualitative inputs are often naively translated into equidistant values in the unit interval. Therefore, the qualitative approach to uncertainty developed in [3][4][5], and the elicitation and the inference methods of Sections 3 and 4 may lead to more robust confidence assessment approaches.…”

“…It is structured as follows. Section 2 presents theoretical background on qualitative capacities that can be viewed as a qualitative counterpart of belief functions, based on [5]. Section 3 deals with the elicitation of qualitative capacities, based on an existing method where linguistic term scales were mapped to belief functions.…”