The importance of dominance and skyline analysis has been well recognized in multi-criteria decision making applications. Most previous studies assume a fixed order on the attributes. In practice, different customers may have different preferences on nominal attributes. In this paper, we identify an interesting data mining problem, finding favorable facets, which has not been studied before. Given a set of points in a multidimensional space, for a specific target point p we want to discover with respect to which combinations of orders (e.g., customer preferences) on the nominal attributes p is not dominated by any other points. Such combinations are called the favorable facets of p. We consider both the effectiveness and the efficiency of the mining. A given point may have many favorable facets. We propose the notion of minimal disqualifying condition (MDC) which is effective in summarizing favorable facets. We develop efficient algorithms for favorable facet mining for different appl...