A new flexible and reliable interval valued fuzzy VIKOR method based on uncertainty risk reduction in decision making process: An application for determining a suitable location for digging some pits for municipal wet waste landfill

• The authors propose the concepts of uncertainty and the risk of uncertainty for the IVFNs.
• The authors present a measurement procedure for the risk of uncertainty related to the IVFNs.
• The authors enter the concepts of uncertainty and the risk of uncertainty in the IVF-MCDM problems.
• The authors propose an IVF-VIKOR method based on uncertainty risk reduction in decision making process.
• The authors apply the proposed method for solving some numerical examples.

Facility location selection problem is one of the challenging and famous kinds of MCDM problems including both quantitative and qualitative criteria. For each Multiple Criteria Decision Making (MCDM) problem, when the ratings of alternatives with respect to the criteria and/or the values of criteria’s weights are presented by Interval Valued Fuzzy Numbers (IVFNs), the conventional fuzzy MCDM methods (Type-1 fuzzy MCDM methods) tend to be less effective. Therefore, the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be applied for solving such fuzzy MCDM problems. In this paper, we propose an IVF-VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method based on uncertainty risk reduction in decision making process. By using such method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving two numerical examples that the former of which is a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The second numerical example is presented with an aim of comparing our method with the two other IVF-MCDM methods. As a result, we found out the proposed method is reliable and practical for the facility location selection problems and other MCDM problems. Moreover, the proposed method has a considerable accuracy and is flexible and easy to use.