Generalized solution principles and out-ranking relations in multi-criteria decision-making

In this paper the abstract notion of a solution principle for multi-criteria decision-making problems is introduced as a set-valued mapping which associates to each decision problem (several) sets of potential solutions. Some modeling conditions are imposed on solution principles which relate them with binary (preference or outranking) relations; this relationship is studied, particularly, the concepts of kernel, quasi-kernel, subsolution and supercore are discussed in terms of solution principles.