Generalized Frame for Orthopair Fuzzy Sets: (m,n)-Fuzzy Sets and Their Applications to Multi-Criteria Decision-Making Methods

Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough soft etc. Indeed, they are successfully employed address partial knowledge, consensus, and borderline cases. One the generalized versions orthopairs is intuitionistic sets which a well-known theory for researchers interested set theory. To extend area application more empirical situations, limitation that grades membership non-membership must be calibrated same power should canceled. this end, we dedicate manuscript introducing frame orthopair called “(m,n)-Fuzzy sets”, will an efficient tool deal issues require different importances degrees cannot addressed by fuzzification tools existing published literature. We first establish its fundamental operations investigate abstract properties can then transmitted various models connection with. Then, rank (m,n)-Fuzzy define functions score accuracy, formulate aggregation operators used sets. Ultimately, develop successful technique “aggregation operators” handle multi-criteria decision-making problems environment The proposed has been illustrated analyzed via numerical example.