Normalized distance–based entropy measures for multiaspect fuzzy soft sets

Multiaspect fuzzy soft sets (MAFSS) is a generalization of fuzzy soft set and multiaspect soft set. It describes objects based on parameters which are associated with different sets of elements characterized by different types of aspect-related universal sets. The parameter-element relationships in a MAFSS are in the form of fuzzy sets. Distance and entropy for fuzzy sets are two important measures that determine the degree of dissimilarity between fuzzy sets and the degree of fuzziness of fuzzy sets, respectively. As MAFSSs are composed of fuzzy sets, the aforementioned measures can be extended to MAFSS environment. In this paper, we present the axiomatic definitions of distance and distance-based entropy for MAFSSs. A general formula for estimating the entropy based on normalized distances is established. Some normalized distance-based entropy measures are derived and their properties are investigated.