Picture Hesitant Fuzzy Set and its Applications

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Kifayat Ullah
Zeeshan Ali
Naeem Jan
Tahir Mahmood
Shahid Maqsood


In this work, we proposed the theory of picture hesitant fuzzy set (PHFS) as a generalization of picture fuzzy set (PFS) and hesitant fuzzy set (HFS). Some basic operations on PHFSs have been developed and their results are studied. These aggregation operators included picture hesitant fuzzy weighted averaging (PHFWA) operator, picture hesitant fuzzy ordered weighted averaging (PHFOWA) operator and picture hesitant fuzzy hybrid averaging (PHFHA) operator. The basic properties of defined aggregation operators have been examined and some important results are discussed. Multi-Attribute decision making (MADM) process is discussed in the environment of PHFSs, and it is illustrated numerically. Finally, some advantages of proposed work are discussed.     

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