C-hypergroupoids obtained by special binary relations

In this paper we deal with the partial or non-partial C-hypergroupoids which are associated with special binary relations defined on H, such as Reflexive, Symmetric, Cyclic and Transitive. Basic properties are investigated and various characterizations are given. The main tool to study the previous special classes of hypergroupoids is the fundamental relation β∗β∗ (i.e. the smallest equivalence relation such that the quotient of a hypergroupoid (partial or not) is a groupoid (partial or not))