Several extensions of fuzzy sets have been proposed in the literature, such as intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, hesitant fuzzy sets and dual hesitant fuzzy sets. In this paper, we set up dual intuitionistic fuzzy sets (OIFS), encompassing all the above fuzzy sets as special cases. Then we investigate the basic operations and properties of OIFS, and propose an extension principle of OIFS. Finally, a practical example about multicriteria group decision making problem is give…
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