F., C., M., J. (2006). QUANTUM THEORY BASED ON FUZZY SETS. The International Conference on Mathematics and Engineering Physics, 3(International Conference on Engineering Mathematics and Physics (ICMEP-3)), 1-12. doi: 10.21608/icmep.2006.29904

CHOVANEC F.; JUREČKOVÁ M.. "QUANTUM THEORY BASED ON FUZZY SETS". The International Conference on Mathematics and Engineering Physics, 3, International Conference on Engineering Mathematics and Physics (ICMEP-3), 2006, 1-12. doi: 10.21608/icmep.2006.29904

F., C., M., J. (2006). 'QUANTUM THEORY BASED ON FUZZY SETS', The International Conference on Mathematics and Engineering Physics, 3(International Conference on Engineering Mathematics and Physics (ICMEP-3)), pp. 1-12. doi: 10.21608/icmep.2006.29904

F., C., M., J. QUANTUM THEORY BASED ON FUZZY SETS. The International Conference on Mathematics and Engineering Physics, 2006; 3(International Conference on Engineering Mathematics and Physics (ICMEP-3)): 1-12. doi: 10.21608/icmep.2006.29904

^{}Associate professor, Dpt. of Natur. Sciences, Academy of Armed Forces, Liptovský Mikuláš, Slovakia.

Abstract

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.