elasticity = (percentage change in Z) / (percentage change in Y)
The smaller the percentage change in Y is practical, the better the measure is and the closer it is to the intended theoretically perfect measure.
Elasticities are often negative, but are sometimes reported in absolute value (perhaps for brevity) in which case the author is depending on the reader knowing, or quickly applying, some theory. Usually the theory is the theory of supply and demand.
Inventing another kind of elasticity is plausible. Doing so implies a partial theory of behavior -- e.g. that Y creates a reason for the agent to change behavior Z.