Hesitant interval-valued intuitionistic fuzzy linguistic set has been developed by extending hesitant fuzzy set, interval-valued intuitionistic fuzzy values and linguistic terms. Some operational laws and distance measures for hesitant interval-valued intuitionistic fuzzy linguistic elements are defined. Several new generalized aggregation operators are proposed for hesitant interval-valued intuitionistic fuzzy linguistic information and some special cases of new operators are studied. Two new multiple attribute decision-making methods have been proposed using new aggregation operators and TOPSIS method. Painting selection problem has been presented to illustrate new methods.
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