Contingency Uniformity Measure: An approach for spread characterization in Contingency tables

This paper introduces the Contingency Uniformity Measure (CUM), a normalized entropy that scales Shannon entropy to the range [0, 1], enabling fair comparisons across contingency tables of different dimensions. CUM retains key properties such as nonegativity, reaches its maximum at the uniform distribution, and satisfies weighted additivity. We formulate and solve three optimization problems, using CUM, under realistic constraints, fixed marginal distributions, a cost matrix, and cost variance. This is demonstrated through a real dataset of cost matrix obtained using distance matrix. Our results show that CUM is an effective, standardized measure for analyzing uncertainty and supporting decision-making in diverse, constraint-driven systems.