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.

This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2015-66471-P and TIN2016-77356-P (MINECO, AEI/FEDER, UE) and by grants VEGA 1/0420/15, VEGA 1/0614/18 and APVV-14-0013.

Peer reviewed