  Coherence measures and their operational interpretations lay the cornerstone
of coherence theory. In this paper, we introduce a class of coherence measures
with $\alpha$-affinity, say $\alpha$-affinity of coherence for $\alpha \in (0,
1)$. Furthermore, we obtain the analytic formulae for these coherence measures
and study their corresponding convex roof extension. We provide an operational
interpretation for $1/2$-affinity of coherence by showing that it is equal to
the error probability to discrimination a set of pure states with the least
square measurement. Employing this relationship we regain the optimal
measurement for equiprobable quantum state discrimination. Moreover, we compare
these coherence quantifiers, and establish a complementarity relation between
$1/2$-affinity of coherence and path distinguishability for some special cases.
