On Bipolar-Valued Hesitant Fuzzy Sets and Their Applications in Multi-Attribute Decision Making

Kifayat Ullah, T. Mahmood, N. Jan, S. Broumi, Q. Khan


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.

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