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Ranking of interval valued intuitionistic fuzzy sets (IVIFSs) plays an important role because of its attraction and applicability to model uncertainty in real life problems. In this article, an attempt has been made to devise a new method for ranking of IVIFSs based on exponential function. The significance of the method is illustrated with the help of some numerical examples and the results are compared with other existing methods. Furthermore, a multi criteria decision making method is presented here to evaluate the final ranking of the alternatives using the proposed ranking method and discussed the consistency of so obtained results.

One of the techniques used to support strong decision making in domains where selection of best alternative is highly complex is the Fuzzy TOPSIS method. In TOPSIS procedure different distance measures are used to calculate the distance of each fuzzy number from both Fuzzy Positive Ideal Solution (FPIS) and Fuzzy negative Ideal Solution (FNIS). In this paper, six well known distance measures have been taken into account which are available in literature and applied to TOPSIS procedure to perform a comparative study throughout numerical problems. The main purpose is to compare the stability and reliability of TOPSIS method in decision science through different distance measures. Fuzzy triangular number is used in our entire case study.

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