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

  • Authors:

  • Zhoujing Wang;Kevin W. Li;Jianhui Xu

  • Affiliations:

  • School of Computer Science and Engineering, Beihang University, Beijing 100083, China and Department of Automation, Xiamen University, Xiamen, Fujian 361005, China;Odette School of Business, University of Windsor, Windsor, Ontario, Canada N9B 3P4;Department of Automation, Xiamen University, Xiamen, Fujian 361005, China

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2011

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Abstract

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