The present complexity approach is based on two assumptions: A1: measurability of deviations of outcomes with respect to reference values; A2; extension of A1 to multi-set analysis. Complexity is then defined in terms of multi-set deviation compared to single-set ones; an interpretation is given in terms of information costs; examples show the relevance of the interpretation. As a useful by-product the explicit solution of the quadratic part of the discrete logistic - one of the examples - is derived; a set of pIJ-numbers is introduced, and a workable method for generating them exposed. Extensions are considered, in particular controllability. A further application is then proposed, namely to hypergraph conflict analysis, in particular conflict resolution. Many decisional conflicts as the spatial level can be axiomatised in this form; it is shown how the use of particular structures - in the mathematical senseof that word - of the problem allows of reducing greatly the degree of complexity of the problem, and hence the difficulty of finding a solution.