Mutual Equidistant-scattering Criterion: a new index for crisp clustering

•A new non-parametric internal validity index is proposed for crisp clustering.•The index is based on within-cluster mutual equidistant-scattering.•It is proved effective on both (4) real-world and (26) synthetic benchmark data sets.•Seven other indexes are employed in comparisons to detect the number of clusters.•The Friedman’s test corroborates that better results are yielded with this proposal.