A Construction of Preference Relation for Models of Decision Making with Quality Criteria

We consider a problem of construction of preference relations for models of decision making with quality criteria. A quality criterion one means as a function from a set of alternatives in some chain (i.e. linearly ordered set). A system of axioms for rule of preferences is given. It is shown that any rule for preferences satisfying these axioms can be presented as a rule for preferences based on some pseudofilter of winning coalitions of criteria. The section 4 contains main results of the article. In particular, necessary and sufficient conditions for transitive and for linear preferences are found. An interpretation of Arrow paradox in terms of filters is given.