Quantification of relevance was studied by Daniel Polani et al. [1,2], building up on Tishby et al. work  on relevant information and the information bottleneck method.Selected references
1. Polani, D., Kim, J.T. and Martinetz, T. An Information-Theoretic Approach for the Quantification of Relevance. In: J. Kelemen and P. Sosik (eds.), Advances in Artificial Life (Proc. 6th European Conference on Artificial Life, Prague, September 10-14), LNCS. Springer 2001
2. Polani, D., Nehaniv, C., Martinetz, T., and Kim, J.T. Relevant Information in Optimized Persistence vs. Progeny Strategies. In M.Rocha, L., Bedau, M., Floreano, D., Goldstone, R., Vespignani, A., and Yaeger, L., editors, Proc. Artificial Life X, 2006.
3. Tishby, N., Pereira, F. C., and Bialek, W. The information bottleneck method. In Proceedings of 37th Annual Allerton Conference on Communication, Control and Computing, Illinois. 1999.