Uncertainties with Atanassov’s intuitionistic fuzzy sets: Fuzziness and lack of knowledge

We review the existing measures of uncertainty (entropy) for Atanassov’s intuitionistic fuzzy sets (AIFSs). We demonstrate that the existing measures of uncertainty for AIFS cannot capture all facets of uncertainty associated with an AIFS. We point out and justify that there are at least two facets of uncertainty of an AIFS, one of which is related to fuzziness while the other is related to lack of knowledge or non-specificity. For each facet of uncertainty, we propose a separate set of axioms. Then for each of fuzziness and non-specificity we propose a generating family (class) of measures. Each family is illustrated with several examples. In this context we prove several interesting results about the measures of uncertainty. We prove some results that help us to construct new measures of uncertainty of both kinds.