On Bipolar-Valued Hesitant Fuzzy Sets and Their Applications in Multi-Attribute Decision Making - Ullah, Kifayat; Mahmood, T.; Jan, N.; Broumi, S.; Khan, Q. (The Nucleus, 2018)
In this manuscript, a novel structure of bipolar-valued hesitant fuzzy set (BPVHFS) is proposed as a generalization of fuzzy set (FS). The basic set theoretic operations of BPVHFSs are defined and their related results are studied. Based on the basic operations, some aggregation operators for BPVHFSs are developed and their fitness is verified using principle of mathematical induction. The multiattribute decision making (MADM) is established in the framework of BPVHFSs and a numerical example is provided to illustrate the process. The article ended with some concluding remarks along with some future directions.