We present and discuss a mixed conjunctive and disjunctive rule, a generalization of conflict repartition rules, and a combination of these two rules. In the belief functions theory one of the major problem is the conflict repartition enlightened by the famous Zadeh's example. To date, many combination rules have been proposed in order to solve a solution to this problem. Moreover, it can be important to consider the specificity of the responses of the experts. Since few year some unification rules are proposed. We have shown in our previous works the interest of the proportional conflict redistribution rule. We propose here a mixed combination rule following the proportional conflict redistribution rule modified by a discounting procedure. This rule generalizes many combination rules.

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This paper is devoted to some selected topics relating Combinatorial Optimization and Hierarchical Classification. It is oriented toward extensions of the standard classification schemes (the hierarchies): pyramids, quasi-hierarchies, circular clustering, rigid clustering and others. Bijection theorems between these models and dissimilarity models allow to state some clustering problems as optimization problems. Within the galaxy of optimization we have especially discussed the following: NP-completeness results and search for polynomial instances; problems solved in a polynomial time (e.g. subdominant theory); design, analysis and applications of algorithms. In contrast with the orientation to "new" clustering problems, the last part discusses some standard algorithmic approaches.