Mathematical programming methodology for multiattribute decision making using interval-valued intuitionistic fuzzy sets

  • Authors:

  • Li-Ling Wang;Deng-Feng Li;Shu-Shen Zhang

  • Affiliations:

  • Key Laboratory of Industrial Ecology and Environmental Engineering MOE, School of Environmental Science and Technology, Dalian University of Technology, Dalian, Liaoning, China;School of Management, Fuzhou University, Fuzhou, Fujian, China;Key Laboratory of Industrial Ecology and Environmental Engineering MOE, School of Environmental Science and Technology, Dalian University of Technology, Dalian, Liaoning, China

  • Venue:
  • Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
  • Year:
  • 2013

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Abstract

Interval-valued intuitionistic fuzzy IVIF sets are a useful tool to deal with fuzziness inherent in decision data and decision making process. The aim of this paper is to develop a methodology for solving multiattribute decision making MADM with both ratings of alternatives on attributes and weights being expressed with IVIF sets. In this methodology, a weighted Euclidean distance between IF sets is defined using weights of IF sets. A pair of nonlinear programming models is constructed based on the concept of the relative closeness coefficients and the distance defined. Two simpler auxiliary nonlinear programming models are further derived to calculate the relative closeness coefficient intervals of alternatives to the IVIF positive ideal solution, which can be used to generate ranking order of alternatives based on the concept of likelihood of interval numbers. The method proposed in this paper is illustrated with a real example.