On the entropy for Atanassov's intuitionistic fuzzy sets: An interpretation from the perspective of amount of knowledge

Given the fact that totally unknown information cannot be expressed by Zadeh's fuzzy sets but can well be represented by Atanassov's intuitionistic fuzzy sets (A-IFSs), we provide in this paper a new idea, from the perspective of amount of knowledge, that the entropy for such information should be unique so that it may differ significantly from the entropy of a particular fuzzy element of which the membership and non-membership values are both equal to 0.5. Motivated by this idea, we present a more strict axiomatic definition of entropy on A-IFSs, and then develop a new entropy measure of A-IFSs that satisfies the refined axioms, with the aim of overcoming some drawbacks and ambiguities the existing entropy brings about and building a new entropy measurement model in the A-IFSs context to show some unique features of A-IFSs from the viewpoint of a specific purpose, notably those related to decision making. This allows us to capture the intrinsic amount of knowledge and the additional features that may be relevant when making decisions, and ultimately may be able to help us distinguish such particular cases in which the membership values are equal to the corresponding non-membership values in the A-IFSs context. Finally, a real-life example is provided for an in-depth discussion on the application of the developed models in decision making under uncertainty. (C) 2014 Elsevier B.V. All rights reserved.