Interval-valued fuzzy strong S-subsethood measures, interval-entropy and P-interval-entropy

In this paper, we introduce the concept of fuzzy interval-entropy. The main feature of this new entropy is that the provided value is a closed subinterval of [0, 1]. This fact has led us to define interval-valued fuzzy strong S-subsethood measures which we use to build fuzzy interval-entropies. As we require that the results of both measures are intervals, we should work with total orders to be able to compare the results. The problem of finding equilibrium points for interval-valued negations with respect to total orders has led us to introduce and study the concept of P-interval-entropy. Finally, in an illustrative example, we discuss an application of the different concepts we have considered. We also compare our results to those obtained in our application where we use the classical interval-valued entropy, which provides a real number instead of an interval as its result, as we know.