An entropy measure definition for finite interval-valued hesitant fuzzy sets

In this work, a definition of entropy is studied in an interval-valued hesitant fuzzy environment, instead of the classical fuzzy logic or the interval-valued one. As the properties of this kind of sets are more complex, the entropy is built by three different functions, where each one represents a different measure: fuzziness, lack of knowledge and hesitance. Using all, an entropy measure for interval-valued hesitant fuzzy sets is obtained, quantifying various types of uncertainty. From this definition, several results have been developed for each mapping that shapes the entropy measure in order to get such functions with ease, and as a consequence, allowing to obtain this new entropy in a simpler way. (C) 2015 Elsevier B.V. All rights reserved.