I. Introduction
Since 1965, the theory of fuzzy set (FS) proposed by Zadeh [1] has achieved a great success in various fields. In FS theory, a membership function of an element to the set indicates the belongingness degree of the element to FS, which is a single value between zero and one. In 1986, Atanassov [2] introduced the concept of an intuitionistic fuzzy set (IFS) characterized by membership and non-membership functions. IFS is more flexible and practical than FS to deal with fuzziness and uncertainty for a very important factor, i.e., the hesitancy function is considered simultaneously. Since then, more and more attentions have been paid on IFS theory and to a wide range of fields IFS has been applied, such as logic programming [3], decision making [4]–[17], medical diagnosis [18],[19], pattern recognition [20]–[23], etc. In the framework of IFS, the decision making problem may be formulated as follows.