QUANTUM THEORY BASED ON FUZZY SETS | ||||
| The International Conference on Mathematics and Engineering Physics | ||||
| Article 1, Volume 3, International Conference on Engineering Mathematics and Physics (ICMEP-3), May 2006, Page 1-12 PDF (518.23 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/icmep.2006.29904 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| CHOVANEC F.; JUREČKOVÁ M. | ||||
| 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. | ||||
| Keywords | ||||
| A D-poset of fuzzy sets; a D-lattice of fuzzy sets; a Bold algebra; a state; an observable | ||||
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