  Data valuation using Shapley value has emerged as a prevalent research domain
in machine learning applications. However, it is a challenge to address the
role of order in data cooperation as most research lacks such discussion. To
tackle this problem, this paper studies the definition of the partial ordinal
Shapley value by group theory in abstract algebra. Besides, since the
calculation of the partial ordinal Shapley value requires exponential time,
this paper also gives three algorithms for approximating the results. The
Truncated Monte Carlo algorithm is derived from the classic Shapley value
approximation algorithm. The Classification Monte Carlo algorithm and the
Classification Truncated Monte Carlo algorithm are based on the fact that the
data points in the same class provide similar information, then we can
accelerate the calculation by leaving out some data points in each class.
