Multiple attribute decision making (MADM) problems often consists of quantitative and qualitative attributes which can be assessed by numerical values and subjective judgments. Subjective judgments can be evaluated by linguistic variables, and both numerical values and subjective judgments can be accurate or uncertain. The evidential reasoning (ER) approach provides a process for dealing with MADM problems of both a quantitative and qualitative nature under uncertainty. The existing ER approach considers both benefit and cost attributes in the evidence combination process. In this paper, deviated interval and fixed interval attributes are introduced into ER based MADM approach and the frames of discernment for representing these two kinds of attributes are given. The transformation rules from the assessment values of deviated interval attributes to belief degrees in the ER structure are then studied. An ave-entropy based weight assignment method considering the risk preference of decision maker is also shown to deal with uncertain assessment situation, such as belief distribution with qualitative attribute and uncertain utility function. Some programming models to generate interval weights and utilities are constructed. The rationality and efficiency of the methods in supporting MADM problems are discussed. Two case studies are provided to demonstrate the applicability and validity of the proposed approaches and the potential in supporting MADM under uncertainty.