Interval type-2 fuzzy sets are associated with greater imprecision and more ambiguities than ordinary fuzzy sets. Decision information provided by the decision-maker is often imprecise or uncertain due to lack of data, time pressure, or the decision-maker’s limited attention and information-processing capabilities. In an interval type-2 fuzzy framework, this paper presents an interactive decision-making method for handling multiple criteria decision analysis problems in which individual assessments are provided as uncertain linguistic variables and the information about criterion weights are not precisely but partially known. Based on the signed distance from the suitability function to the anti-ideal reference point, this paper constructs an integrated programming model as a core decision-making method within the environment of interval type-2 trapezoidal fuzzy numbers under incomplete weight information. In addition, this paper develops an interactive procedure by utilizing the information of the decision-maker’s ordered paired comparison judgments between the alternatives for the sake of a satisfactory solution. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a practical example of landfill site selection.

interval type-2 fuzzy set, interactive decision-making method, multiple criteria decision analysis, incomplete weight information.