Aspects of generalized orthopair fuzzy sets

We introduce the idea of orthopair membership grades and the related idea of general orthopair fuzzy sets. It is noted that these generalize the intuitionistic and Pythagorean fuzzy sets by allowing the support for and against membership to be almost anywhere in [0, 1]x[0, 1], giving systems modelers great freedom in capturing human knowledge. The aggregation of generalized orthopair fuzzy sets is considered with particular concern for the OWA and Choquet aggregation. The concepts of possibility and certainty as well as plausibility and belief are investigated in this general orthopair environment. We study arithmetic operations on general orthopair fuzzy sets. We show how to obtain associated interval valued fuzzy sets from general orthopair fuzzy sets.