A Kind of Non-associative Groupoids and QuasiNeutrosophicExtended TripletGroupoids(QNET-Groupoids)

Abstract

The various generalized associative laws can be considered as generalizations of traditional symmetry.Based on the theories of CA-groupoid, TA-groupoid and neutrosophic extended triplet (NET), this paper first proposes a new concept, which is type-2 cyclic associative groupoid (shortly by T2CA-groupoid), and gives some examples and basic properties. Furthermore, as a combination of neutrosophic extended triplet group (NETG) and T2CA-groupoid, the notion of type-2 cyclic associative neutrosophic extended triplet groupoid (T2CA-NET-groupoid) is introduced, and a decomposition theorem of T2CA-NET-groupoid is proved. Finally,as a generalization of neutrosophic extended triplet group (NETG), the concept of quasi neutrosophic extended triplet groupoid (QNET-groupoid) is introduced, and the relationships among T2CA-QNET-groupoid, T2CA-NET-groupoid and CA-NET-groupoid are discussed.