Extension of the TOPSIS for Multi-Attribute Group Decision Making under Atanassov IFS Environments

This paper extends the technique for order preference by similarity to ideal solution TOPSIS for solving multi-attribute group decision making MAGDM problems under Atanassov intuitionistic fuzzy set IFS environments. In this methodology, weights of attributes and ratings of alternatives on attributes are extracted from fuzziness inherent in decision data and making process and described using Atanassov IFSs. An Euclidean distance measure is developed to calculate the differences between alternatives for each decision maker and an Atanassov IFS positive ideal solution IFSPIS as well as an Atanassov IFS negative ideal-solution IFSNIS. Degrees of relative closeness to the Atanassov IFSPIS for all alternatives with respect to each decision maker in the group are calculated. Then all decision makers in the group may be regarded as "attributes" and a corresponding classical MADM problem is generated and hereby solved by the TOPSIS. The proposed methodology is validated and compared with other similar methods. A numerical example is examined to demonstrate the implementation process of the methodology proposed in this paper.