Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems

The case of mixed data in which attributes have a different nature is not well known in current literature, although it is essential from a practical point of view. This situation is particularly frequent in risk management modelling which incorporates various degrees of precision of the variables measured, and can also be noted in a planning context for project evaluation problems taking into account information of a mixed (qualitative and quantitative) type. For a set of alternatives evaluated by a set of attributes, three kinds of evaluations are considered in this paper: deterministic, stochastic, or fuzzy with relation to each attribute. The mixed-data multi-attribute dominance for a reduced number of attributes is proposed to model the preferences in this kind of problem. The approach is based on the dominance-based rough set approach proposed by Greco, Matarazzo and Slowinski.