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A new approach to representation of observables on fuzzy quantum posets

Le Ba Long
1992 Applications of Mathematics  
It is obvious that a fuzzy quantum space is a fuzzy quantum poset, and a model I of a fuzzy quantum poset is a model II, but the converse is not true, in general, as we can see below. Example 1.  ...  Let (Q, M) be a model I or II of fuzzy quantum posets. Let a be a given fuzzy set of M.  ... 
doi:10.21136/am.1992.104516 fatcat:ajcxzqgtwbch5hnu7mwoepvwbi

Page 5777 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
Thus any quantum poset is also a fuzzy quantum poset. There also ex- ist fuzzy quantum posets that are essentially fuzzy (i.e., for some of their propositions the truth value is from (0,1)).  ...  A definition of a fuzzy quantum poset [Lé ba Long, Acta Math. Univ.  ... 

QUANTUM THEORY BASED ON FUZZY SETS

CHOVANEC F., JUREČKOVÁ M.
2006 The International Conference on Mathematics and Engineering Physics  
The basic notions of the quantum logic theory -a state and an observable are defined in D-posets of fuzzy sets.  ...  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.  ...  Then F is a fuzzy-q-σ-algebra and ( X , F) is an F-quantum poset. F-quantum spaces and F-quantum posets were studied by many authors.  ... 
doi:10.21608/icmep.2006.29904 fatcat:rtqccke33reqrjfe3z63ibn4qu

Page 6417 of Mathematical Reviews Vol. , Issue 97J [page]

1997 Mathematical Reviews  
The main ideas are that quantum mechanics is a mechanics whose underlying logic is a fuzzy logic, and classical mechanics is a crisp limit of quantum mechanics based on fuzzy logic.  ...  Another topic of the paper is quantum computing and its con- nection with quantum mechanics and fuzzy logic.  ... 

Page 1699 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
An example of a quasi-orthocomplemented poset that is not a g-orthocomplemented poset is an F-quantum poset {[A. Dvuretenskij and F. Chovanec, Internat. J. Theoret.  ...  A quasi-orthocomplemented poset P is a generalization of a o- orthocomplemented poset.  ... 

Page 5107 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
Further, extending the funda- mental notions of quantum logics theory, they define observables and states on D-o-posets as D-o-poset-structure-preserving map- pings respectively from the o-algebra @(R)  ...  He proves that every such h-fuzzy quantum logic is actually a quantum logic, and provides some reasonable arguments in favor of his hypothesis that another choice of operations will not lead to a quantum  ... 

Preface of the guest editors

Ferdinand Chovanec, Olga Nánásiová, Alexander Šostak
2009 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
Among utilized models, we can find orthomodular lattices (quantum logics), difference posets (effect algebras), multivalue algebras and fuzzy sets.  ...  In the first paper ''Conditional states and independence in D-posets'' by authors Chovanec Ferdinand, Drobná Eva, Kôpka František and Nánásiová Olga (Slovakia) conditional states on difference posets are  ... 
doi:10.1007/s00500-009-0486-1 fatcat:23k6k5h4jzfcdmmeos7vqawfkm

Geometric viewpoint on the quantization of a fuzzy logic [article]

Davide Pastorello
2020 arXiv   pre-print
Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum  ...  phase space) obtaining a quantized version of a fuzzy logic by deformation of the product t-norm.  ...  from a class of fuzzy sets such that the compatibility in the poset is related to the commutation w.r.t. ⋆.  ... 
arXiv:2004.03395v1 fatcat:f2kvbxfwrza6pla7v63lfphluq

Fuzzification of probabilistic objects

Martin Papco
2013 Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology  
Using our previous results, we show that the category ID of D-posets of fuzzy sets provides a framework in which the transition from classical to fuzzy probability theory is the consequence of some natural  ...  We introduce two categories CP and FP of probability spaces and observables corresponding to the classical probability theory and the fuzzy probability theory, respectively.  ...  Such observables correspond to genuine fuzzy (operational) random variables and have definite quantum qualities.  ... 
doi:10.2991/eusflat.2013.10 dblp:conf/eusflat/Papco13 fatcat:6r5vdfhmijd77acrgq2nuy7lau

Page 4476 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
Fuzzy Math. 10 (2002), no. 3, 587-599. The paper deals with fuzzy topology on bounded posets, or- thocomplemented posets, orthomodular posets, and a-complete orthomodular posets (quantum logics).  ...  topological convergence for sequences in bounded posets and related structures.  ... 

Page 9558 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
The authors introduce the notion of negative difference on a poset and discuss the interrelations between fuzzy implication algebras and negative differences posets. Sam L.  ...  and fuzzy implication algebras.  ... 

Page 6309 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
Maczynski (Warsaw) 96j:81017 81P10 03B52 03G12 06C15 Mesiar, Radko (SK-STU; Bratislava) Do fuzzy quantum structures exist?  ...  Pykacz developed several axiomatic systems of fuzzy logics describing quantum systems. One of these [Internat. J. Theoret.  ... 

Page 638 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
Fuzzy Sets and Systems 33 (1989), no. 2, 165-190. This paper is a study of Brouwer-Zadeh posets (BZ-posets).  ...  The first of these, called also the Zadeh orthocomplementation, is a gen- eralization of the orthocomplementation of fuzzy set theory.  ... 

Page 3783 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
The possibly fuzzy or unsharp events affiliated with a physical system can be represented in a D-test space and, if the D-test space is algebraic, the elements of the corresponding D-poset can 81P Axiomatics  ...  between D-test spaces and D- posets to investigate the algebraic tensor product of D-posets.  ... 

Page 11 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
Pulmannova, Some properties of transition amplitude spaces (pp. 119-123); Jaroslaw Pykacz, Probability measures in the fuzzy set approach to quantum logics (pp. 124-128); Z.  ...  Rietanova, Some properties of topology in quantum logics induced by measures (pp. 129-132); Vladimir Rogalewicz and Mirko Navara, On constructions of orthomodular posets (pp. 133-137); Gottfried T.  ... 
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