Modeling rational decisions in ambiguous situations: a multi-valued logic approach

If a decision context is completely precise, making good decisions is relatively easy. In the presence of ambiguity, rational decision-making is incomparably more challenging. We understand ambiguous situations as cases, where the decision-maker has imprecise (uncertain or vague) knowledge that is acquired from incomplete information (without limiting it to probability judgements as in common terminology). From that, we assume that imprecisions in knowledge can affect all elements of the decision field as well as the objective function. For the modeling of such decision situations, classical logics are no longer considered as means of choice, so that we suggest using approaches from the field of multi-valued logic. In the present work, we take suitable calculi from the so-called intuitionistic fuzzy logic into account. On that basis, we propose a model for the formulation and solving of decision problems under ambiguity (in the general sense). Particularly, we address decision situations, in which a decision-maker has sufficient information to specify point probability values, but insufficient information to express point utility values. Our approach is also applicable for modeling cases in which the probability judgments or both, probability and utility judgements are imprecise. Our model is novel in that we combine core elements of established approaches for the formal handling of uncertainty (maxmin and $$ \alpha $$ α -maxmin expected utility models) with the mathematical foundation of intuitionistic fuzzy theory.