The MAP metric generates the overall performance in precision, recall and ranking.
It is known that every metric generates an S-metric, and in [10], it was given an example of an S-metric which is not generated by a metric.
The D metric generates a value that usually lies between 0 and 1, where a value of 1 indicates that the trait has evolved in essentially a random manner (i.e. no phylogenetic signal), and 0 indicates that the trait is highly correlated with phylogeny, in a manner predicted by Brownian motion.
The metric generated by the norm (3) on (H_{alpha}) is called the Hölder metric.
We call this metric (d_{S}) as the metric generated by S in the case (d_{S}) is a metric.
The manifold M can be interpreted as a Riemannian manifold (M, g) where g is the metric generated by a x, D).
Moreover, if we put J = d, where d : X × X → [ 0, ∞ ) is the usual metric, then N J is a fuzzy metric generated by d.
Let (X, S) be a complete S-metric space, ((X,d_{S})) be the metric space obtained by the metric generated by S, and T be a self-mapping of X.
It follows from [1, 2] that if ω is a modular on X, then the modular space X ω can be equipped with a (nontrivial) metric generated by ω and given by d ω ( x, y ) = inf { λ > 0 : ω λ ( x, y ) ≤ λ }. for any x, y ∈ X ω.
It follows from [9, 10] that if ω is a modular on X, then the modular space (X_{omega}) can be equipped with a (nontrivial) metric, generated by ω and given by d_{omega} x,y)= infbigl{ lambda>0: omega_{ lambda} x,y) leq lambda bigr} for any (x, y in X_{omega}).
It follows from [1, 2] that if w is a modular on X, then the modular space X w can be equipped with a (nontrivial) metric, generated by w and given by d w ( x, y ) = inf { λ > 0 : w λ ( x, y ) ≤ λ }. for any x, y ∈ X w.
