Towards a Probability Theory on Nuanced MV-Algebras
Lavinia Corina Ciungu
In this paperweintroduce a new concept of probability (state) on n-nuanced MV-algebras and we prove some of its properties. As a main result, we prove that there is a one-to-one correspondence between the set of states on an n-nuanced MV-algebra L and the set of states of its MV-center M(L). We also introduce the notion of a conditional state on an n-nuanced MValgebra L and we prove that the computation of a conditional state on L can be reduced to the computation of the state obtained by restriction to M(L).We define the notion of a continuous state on L based on the order convergence and we prove that any continuous state is a submeasure.
Keywords: Nuanced MV-algebra, Probability, State, Conditional state, Conditional probability, Order convergence, Continuous state, Submeasure.
AMS Subject Classification 2000: 03G20, 06D30