@article{Ullah_Mahmood_Jan_Broumi_Khan_2018, title={On Bipolar-Valued Hesitant Fuzzy Sets and Their Applications in Multi-Attribute Decision Making}, volume={55}, url={http://thenucleuspak.org.pk/index.php/Nucleus/article/view/417}, abstractNote={In this manuscript, a novel structure of bipolar-valued hesitant fuzzy set (BPVHFS) is proposed as a<br />generalization of fuzzy set (FS). The basic set theoretic operations of BPVHFSs are defined and their<br />related results are studied. Based on the basic operations, some aggregation operators for BPVHFSs<br />are developed and their fitness is verified using principle of mathematical induction. The multiattribute<br />decision making (MADM) is established in the framework of BPVHFSs and a numerical<br />example is provided to illustrate the process. The article ended with some concluding remarks along<br />with some future directions.}, number={2}, journal={The Nucleus}, author={Ullah, Kifayat and Mahmood, T. and Jan, N. and Broumi, S. and Khan, Q.}, year={2018}, month={Oct.}, pages={93–101} }