ABSTRACT
A new probability model based on the theory of fuzzy sets is presented. In this
model, a difference of comparable fuzzy sets is the primary operation. The idea of
a difference of fuzzy sets (fuzzy events) is simple: If we have two comparable events
a and b ( a ≤ b ), then our knowledge on a and b entails the complete knowledge of
the complement of a in b , i. e., b ⊖ a .
The new algebraic structure of fuzzy sets is called a difference poset (a D-poset) of
fuzzy sets. Some properties of a lattice ordered D-poset of fuzzy sets (a D-lattice of
fuzzy sets) are studied. An MV-algebra of fuzzy sets (a Bold algebra) is characterized
in the D-poset of fuzzy sets set-up. The sufficient and necessary conditions for a Dlattice
of fuzzy sets to be a Bold algebra are given. The basic notions of the quantum
logic theory - a state and an observable are defined in D-posets of fuzzy sets.