Totally monotone core and products of monotone measures Original Research Article

Several approaches to the product of non-additive monotone measures (or capacities) are discussed and a new approach is proposed. It starts with the Möbius product [E. Hendon, H.J. Jacobsen, B. Sloth, T. Tranæs, The product of capacities and belief functions, Mathematical Social Sciences 32 (1996) 95–108] of totally monotone measures and extends it by means of a supremum to general monotone measures. The sup runs over sets of totally monotone measures. These sets are defined like the core of monotone measures (or cooperative games). The new product is compatible with the partial order ⩽ for arbitrary monotone measures.