In this paper we develop a new measure for calculating the correlation coefficients between intuitionistic fuzzy sets (IFSs), and prove its desirable axiomatic properties. Then we present an algorithm for multi-attribute decision making. The algorithm first defines the intuitionistic fuzzy ideal solution (IFIS) and the intuitionistic fuzzy negative ideal solution (IFNIS). Then based on the IFIS, the IFNIS and the developed correlation coefficient, the algorithm gives a simple and straightforward method to rank and select the given alternatives. Two numerical examples are used to illustrate our algorithm. Finally we extend the correlation coefficient and the algorithm to interval-valued intuitionistic fuzzy environment.
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