Measures of embedding for interval-valued fuzzy sets

Interval-valued fuzzy sets are a generalization of classical fuzzy sets where the membership values are intervals. The epistemic interpretation of interval-valued fuzzy sets assumes that there is one real-valued membership degree of an element within the membership interval of possible membership degrees. Considering this epistemic interpretation, we propose a new measure, called IV-embedding, to compare the precision of two interval-valued fuzzy sets. An axiomatic definition for this concept as well as a con-struction method are provided. The construction method is based on aggregation operators and the concept of interval embedding, which is also introduced and deeply studied.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).