QUANTUM THEORY BASED ON FUZZY SETS
Ferdinand Chovanec, Mária Jurečkova
A new probability model based on the theory of fuzzy sets is presented. In thismodel, a difference of comparable fuzzy sets is the primary operation. The idea ofa difference of fuzzy sets (fuzzy events) is simple: If we have two comparable eventsa and b ( a ≤ b ), then our knowledge on a and b entails the complete knowledge ofthe complement of a in b , i. e., b ⊖ a .The new algebraic structure of fuzzy sets is called a difference poset (a D-poset) offuzzy sets. Some properties of a lattice ordered D-poset of fuzzy sets (a D-lattice offuzzy sets) are studied. An MV-algebra of fuzzy sets (a Bold algebra) is characterizedin the D-poset of fuzzy sets set-up. The sufficient and necessary conditions for a Dlatticeof fuzzy sets to be a Bold algebra are given. The basic notions of the quantumlogic theory - a state and an observable are defined in D-posets of fuzzy sets.
The International Conference on Mathematics and Engineering Physics/The International Conference on Mathematics and Engineering Physics•May 1, 2006•0 citations