Discrete transformation hypergroups and transformation hypergroups with phase tolerance space

Enumeration of Varlet and Comer Hypergroups

“…An algebraic hyperstructure is a natural generalization of a classical algebraic structure. More precisely, an algebraic hyperstructure is a non-empty set H endowed with one or more hyperoperations that associate with two elements of H not an element, as in a classical structure, but a subset of H. One of the interests of the researchers in the field of hyperstructures is to construct new hyperoperations using graphs [18], binary relations [2,5,7,8,9,11,15,21,23], n-ary relations [10], lattices [16], classical structures [13], tolerance space [12] and so on. Connections between lattices and hypergroupoids have been considered since at least three decades, starting with [24] and followed by [3,14,17].…”

From Automata to Multiautomata via Theory of Hypercompositional Structures

“…The generalizations of algebraic automata in the sense of the theory of hypercompositional structures first focused on constructions of commutative hypergroups on their state sets. Properties of automata have been described by means of properties of such hypergroups over their state sets; see, e.g., [5,[10][11][12]. The next step is to construct hypercompositional structures on the input sets and generalize the MAC condition to GMAC.…”

Enumeration of Rosenberg hypergroups

“…More precisely, an algebraic hyperstructure is a nonempty set H endowed with one or more hyperoperations that associate with two elements of H not an element, as in a classical structure, but a subset of H. One of the interests of the researchers in the field of hyperstructures is to construct new hyperoperations using graphs [1], automata [2], binary relations [3][4][5][6][7][8][9][10][11], n-ary relations [12,13], lattices [14,15], classical structures [16,17], tolerance space [18] and so on. This paper deals with hypergroupoids derived from binary relations, in particular we study some properties of the hypergroups introduced by Rosenberg [10] and called here Rosenberg hypergroups.…”