Monotonic functional mapping

I have n functions f_i(x){i=1,...,n} which do not preserve the monotonic mapping order i.e. if x_1 < x_2, then in general, f_i(x_1) is not less than f_i(x_2) (for all i = 1,2,...n). So can I construct a function g mapping on fi's such that g(f1,f2,...fn) is monotonic? If yes, please elaborate on the method for the same. Even if g is a unimodal function, it should be fine.

Put differently, for every value of x over an interval, I have the (n) outcomes of some physical process denoted by f_i (i = 1,2, ..., n). Now given such a set of f_i's corresponding to an unknown value of x (but known to lie within an interval), I have the task of estimating x. Since these f_i's are not monotonic in nature (no set pattern), I felt it would aid in this estimation task of mine if I could construct a monotonic function g using the f_i's.

Please do convey your ideas.