Fuzzy multi-attribute decision making under interval number

Multi-attribute decision making (MADM) is important in many domains where fuzzy and uncertain information are involved Usually decision makers are willing or able to provide interval information, because of lack of knowledge or data, their limited experience or time pressure. The research about fuzzy MADM under interval number has become an active branch in decision making science. After introducing some primary concepts, this paper discuss two methods that deal with fuzzy MADM whose attribute weights and attribute values are expressed in the form of interval number. The first method based on programming model is a typical method, having a more complicated calculation procedure, compared with the second method based on stochastic simulation. In order to illuminate these two methods clearly, principles and calculation steps of both methods are introduced In the end of each method's discussion, one real application example in choosing shipping modes for the adaptability of satisfying cargo owners' requirements is given, in order to testify each method's feasibility.