Approximate reasoning with generalized orthopair fuzzy sets

We introduce the idea of generalized orthopair fuzzy sets, which provide an extension of intuitionistic fuzzy sets. The basic properties of these generalized orthopair fuzzy sets are discussed. We discuss the use of these sets in knowledge representation. We consider the use of these types of orthopair fuzzy sets as a basis for the system of approximate reasoning introduced by Zadeh. This is referred to as OPAR. The basic operations of OPAR are introduced. A reasoning mechanism in OPAR, based on the idea of entailment, is provided. We look at the formulation of the ideas of possibility and certainty using these orthopair fuzzy sets.