Multi-attribute decision making models under interval type-2 fuzzy environment

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the decision information in the process of decision making. In this article, we investigate the decision making problems in which all the information provided by the decision maker is expressed as interval type-2 fuzzy decision matrix where each of the elements is characterized by interval type-2 fuzzy set, and the information about attribute weights is partially known, which may be constructed by various forms. We first utilize the average centroid measure to calculate the average centroid of each attribute value and construct the average centroid matrix of the interval type-2 fuzzy decision matrix. Based on the average centroid matrix and the given attribute weight information, we establish some optimization models to determine the weights of attributes. Furthermore, we develop a procedure to identify the best alternative(s). Finally, we give an illustrative example.