Function/Operation Definitions

Question

If I want to define a function/operation for equivalence classes, is it permissible to stipulate contingencies based upon element characteristics or does dependency on the choice of element characteristics invalidate the definition? A possible example:
if b > a, then (a,b)+(c,d) = ab+cd
and
if b < a, then (a,b)+(c,d) = abc+d, etc.