On multisemigroups
  Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for multisemigroups. Special attention is paid to simple and nilpotent multisemigroups. We also show that "almost all" randomly chosen multivalued binary operations define multisemigroups. 
Ganna Kudryavtseva and Volodymyr Mazorchuk
math.GR math.CT