A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information

9 This article proposes an approach to handle multi-attribute decision making (MADM) 10 problems under the interval-valued intuitionistic fuzzy environment, in which both 11 assessments of alternatives on attributes (hereafter, referred to as attribute values) and 12 attribute weights are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). 13 The notion of relative closeness is extended to interval values to accommodate IVIFN 14 decision data, and fractional programming models are developed based on the Technique 15 for Order Preference by Similarity to Ideal Solution (TOPSIS) method to determine a 16 relative closeness interval where attribute weights are independently determined for each 17 alternative. By employing a series of optimization models, a quadratic program is 18 established for obtaining a unified attribute weight vector, whereby the individual IVIFN 19 attribute values are aggregated into relative closeness intervals to the ideal solution for 20 final ranking. An illustrative supplier selection problem is employed to demonstrate how 21 to apply the proposed procedure. 22