On Some Applications of the Vougiouklis Hyperstructures to Probability Theory

Abstract

Some important concepts about algebraic hyperstructures, especially from a geometric point of view, are recalled. Many applications of the Hv structures, introduced by Vougiouklis in 1990, to the de Finetti subjective probability theory are considered. We show how the wealth of probabilistic meanings of Hv-structures confirms the importance of the theoretical results obtained by Vougiouklis. Such results can be very meaningful also in many application fields, such as decision theory, highly dependent on subjective probability.

Keywords

• algebraic hyperstructures
• subjective probability
• Hv structures
• join spaces