Discrete transformation hypergroups and transformation hypergroups with phase tolerance space

Tolerance spaces and algebraic structures with compatible tolerances play an important role in contemporary algebra and their applications. In this contribution we are presenting transformation hyperstructures, namely semihypergroups and hypergroups, acting on tolerance spaces. Some basic concepts concerning the mentioned structures are introduced and their fundamental properties are examinated on suitable constructions. Transformation groups which represent the classical and developing discipline are situated in the intersection of several parts of mathematical structures (see e.g. [11],[12],[16]). In this contribution we generalize in a certain sense the classical concept of action of a group on a given phase space. We are presenting transformation hyperstructures, namely semihypergroups and hypergroups, some of them acting on tolerance spaces. One of the motivating factors in developing the theory of hyperstructures was the generalization of concepts of classical mathematical struc...

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Sárka Hosková, Jan Chvalina
• Keywords: DM 2008, Tolerance, Tolerance Spaces, Transformation Hyperstructures