Continuous Coalition Structure Generation in Relational Dependency Games via Rough Set Valuation and Agree Sets

Relational dependency coalitional games, RGs, provide a framework for modeling coalition formation in which agent dependencies are governed by relational database constraints. However, existing RG models are often formulated as simple games with binary valuations, where coalitions are classified as winning or losing based on superkey properties. This binary view does not capture partial information gain in noisy, incomplete, or real-world decision data. This paper introduces a continuous valuation framework for RGs based on rough set theory. The characteristic function is defined as the quality of classification derived from tuple agree sets. We prove that the valuation is monotonic. We also show, through an explicit XOR-style counterexample, that the valuation is not submodular in general, and we identify a restricted coverage-separability condition under which submodularity holds. Based on this valuation, we describe a dynamic programming framework and evaluate Exact DP, DP-AB, SG-CSG, and SG-CSG+. Exact DP disables heuristic pruning and provides the certified reference welfare. DP-AB is an ablated DP variant with caching and heuristic singleton-sum pruning. SG-CSG is a polynomial-time pairwise greedy heuristic, while SG-CSG+ extends it with triple-merge lookahead and random restarts. Experiments on toy, synthetic, and real-world decision tables show that SG-CSG can obtain high welfare on instances with low-order dependency structure but can fail when positive coalition value arises only from higher-order coalitions. SG-CSG+ mitigates this failure on the high-synergy synthetic instance. Real-world experiments on Play Tennis, Iris, and the UCI Wine dataset ( \(\:n=13\) attributes), together with external-style generic baselines LS-CSG and SA-CSG, demonstrate the interpretability, scalability, and practical behavior of the framework. The inclusion of the mid-scale Wine dataset provides a rigorous stress-test of the heuristic escape capabilities and Exact DP scalability. A unified supplemental simulation provides the code, output, and metadata used to reproduce all reported results.