Identifying and eliminating dominated alternatives in multi-attribute decision making with intuitionistic fuzzy information

Multi-attribute decision making under uncertainty is a usual task in our daily life. In the decision making process, the decision information provided by the decision maker (or expert) over alternatives may take the form of intuitionistic fuzzy numbers, and the weight information on attributes is usually incomplete. To this issue, we first transform the original decision matrix, whose elements are intuitionistic fuzzy numbers expressed by pairs of satisfaction degrees and dissatisfaction degrees, into its expected decision matrix, whose elements are composed of satisfaction degrees and hesitation degrees. We introduce the concept of dominated alternative, and give a method to identify the dominated alternatives. Then we develop an interactive method for eliminating any dominated alternatives by updating the decision maker's preferences gradually so as to find out the optimal one eventually. A further extension of the interactive method to interval-valued intuitionistic fuzzy situations is given, and the solution process of this interactive method is shown in detail through an illustrative example.

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