Research on Hamacher Operations for q-rung Orthopair Fuzzy Information

Research on q-rung orthopair fuzzy information aggregation serves as a significant part of the q-rung orthopair fuzzy set theory. Note that the aggregation operators are built on operations over q-rung orthopair fuzzy values. Recently, the Hamacher operations, generalizations of algebraic and Einstein operations, on q-rung orthopair fuzzy information were proposed. In this paper, we give an exhaustively theoretical analysis of these developed operations for q-rung orthopair fuzzy values. Particularly, we investigate the operational rules of q-rung orthopair fuzzy Hamacher operations, and the results are consistent with our expectation. Thus the meaningfulness of these operations is confirmed, which provides a solid fundamental basis for further studies. Moreover, the monotonicity and limiting cases of these operations with respect to parameters contained therein are examined.