A total uncertainty measure for Atanassov’s intuitionistic fuzzy sets

Abstract

The amount of uncertainty is important to assess the information related to uncertainty theory such as fuzzy sets. Uncertainty measure of Atanassov’s intuitionistic fuzzy sets has attracted the attention of researchers for decades. Most of proposed uncertainty measures are related to entropy measure. However, the relation between uncertainty and entropy cannot be well described, especially for the intuitionistic fuzzy sets. Other uncertainty measures developing form distance measures have the risk of information loss in applications related to decision making. In this paper, a new uncertainty measure was proposed for intuitionistic fuzzy sets, named as total uncertainty. The axiomatic properties of uncertainty measure are extended. The characteristics of the new total uncertainty measure are analyzed through strict mathematical proof and numerical examples.