Abstract
The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based on t-conorms and t-norms are proposed, which can be used to aggregate decision-makers' information in multicriteria decision-making (MCDM) problems. Some valuable proposals of these operators are studied. In particular, based on algebraic and Einstein t-conorms and t-norms, some hesitant interval-valued intuitionistic fuzzy algebraic aggregation operators and Einstein aggregation operators can be obtained, respectively. Furthermore, an approach of MCDM problems based on the proposed aggregation operators is given using hesitant interval-valued intuitionistic fuzzy information. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the developed approach, and the study is supported by a sensitivity analysis and a comparison analysis.
Highlights
Since fuzzy sets were proposed by Zadeh [1], the studies on multicriteria decision-making (MCDM) problems have made great progress
hesitant fuzzy sets (HFSs) are the extension of traditional fuzzy sets, and their membership degree of an element is a set of several possible values between 0 and 1
Precise numerical values in HFSs can be replaced by interval-valued intuitionistic fuzzy sets (IVIFSs), which provide more preference information for decision-makers
Summary
Since fuzzy sets were proposed by Zadeh [1], the studies on multicriteria decision-making (MCDM) problems have made great progress. Atanassov [9] introduced the operators of IVIFSs. Lee [10] proposed a method for ranking interval-valued intuitionistic fuzzy numbers (IVIFNs) for fuzzy decisionmaking problems. Chen et al [28] generalized the concept of HFSs to hesitant intervalvalued fuzzy sets (HIVFSs) in which the membership degrees of an element to a given set are not exactly defined but denoted by several possible interval values. Comparing to the existing fuzzy sets mentioned above, HIVIFSs are a new extension of HFSs, which support a more flexible and simpler approach when decision-makers provide their decision information in a hesitant interval-valued intuitionistic fuzzy environment.
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