A multi-criteria decision problem based on information uncertainty conveyed by intuitionistic interval-valued fuzzy sets

Abstract In a multi-criteria decision problem, represented by intuitionistic interval-valued fuzzy sets that cannot be properly ranked linearly, it is not always possible to adequately estimate the uncertainty of information using a single-degree scalar measure. We analyze four different ways of quantifying information uncertainty, using an overall measure and three types of directional measures. The assessment of different types of information uncertainty is performed in the context of hypothetical and possible changes in the degree of membership and non-membership for a given degree of hesitation of an element in the set (i.e. in terms of permissible changes in the assessment of information uncertainty). This approach allows for taking into account the asymmetric nature of the assessment of changes in information uncertainty, perceived in the real physical world from a human perspective. We propose a ranking method for alternatives/options (separately for each type of information uncertainty), which, additionally, allows for taking into account the level of information certainty in the process of selecting the best alternative. We analyze examples meant to illustrate our approach and show that it allows for the analysis of alternatives from four complementary perspectives based on information uncertainty, something that currently used methods cannot do. We present an example illustrating the comparison of our results with selected results from the literature.