Decision making with distance and cosine similarity measures for intuitionistic hesitant fuzzy sets
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The definition of intuitionistic hesitant fuzzy sets(IHFSs) is developed based on intuitionistic fuzzy sets(IFSs) and hesitant fuzzy sets(HFSs) and it allows the membership of an element to be a set of several possible intuitionistic fuzzy values. The intuitionistic hesitant fuzzy sets(IHFSs) is a new and flexible tool in representing hesitant information in decision making. Distance and cosine similarity measures have been applied widely in many research domains and practical fields. In this paper, we firstly proposed some distance and similarity measures for IHFSs based on Hamming distance, Euclidean distance and generalized distance, especially, a new cosine similarity measure for IHFSs is proposed and the corresponding cosine distance measures are given. It is shown that all three parameters (membership degree, non membership degree and degree of hesitation) describing intuitionistic hesitant fuzzy sets should be taken into account when calculating those distance and cosine similarity measures. In the end, a new cosine similarity measure and distance measures are applied to multiple attribute decision-making.
Abstract
The definition of intuitionistic hesitant fuzzy sets(IHFSs) is developed based on intuitionistic fuzzy sets(IFSs) and hesitant fuzzy sets(HFSs) and it allows the membership of an element to be a set of several possible intuitionistic fuzzy values. The intuitionistic hesitant fuzzy sets(IHFSs) is a new and flexible tool in representing hesitant information in decision making. Distance and cosine similarity measures have been applied widely in many research domains and practical fields. In this paper, we firstly proposed some distance and similarity measures for IHFSs based on Hamming distance, Euclidean distance and generalized distance, especially, a new cosine similarity measure for IHFSs is proposed and the corresponding cosine distance measures are given. It is shown that all three parameters (membership degree, non membership degree and degree of hesitation) describing intuitionistic hesitant fuzzy sets should be taken into account when calculating those distance and cosine similarity measures. In the end, a new cosine similarity measure and distance measures are applied to multiple attribute decision-making.
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