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A new approach to representation of observables on fuzzy quantum posets

1992
*
Applications of Mathematics
*

It is obvious that a

doi:10.21136/am.1992.104516
fatcat:ajcxzqgtwbch5hnu7mwoepvwbi
*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. ...##
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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. ...##
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QUANTUM THEORY BASED ON FUZZY SETS

2006
*
The International Conference on Mathematics and Engineering Physics
*

The basic notions of the

doi:10.21608/icmep.2006.29904
fatcat:rtqccke33reqrjfe3z63ibn4qu
*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. ...##
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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. ...##
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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*. ...##
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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

2009
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Soft Computing - A Fusion of Foundations, Methodologies and Applications
*

Among utilized models, we can find orthomodular lattices (

doi:10.1007/s00500-009-0486-1
fatcat:23k6k5h4jzfcdmmeos7vqawfkm
*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 ...##
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Geometric viewpoint on the quantization of a fuzzy logic
[article]

2020
*
arXiv
*
pre-print

Considering the geometric formulation of

arXiv:2004.03395v1
fatcat:f2kvbxfwrza6pla7v63lfphluq
*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. ⋆. ...##
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Fuzzification of probabilistic objects

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-

doi:10.2991/eusflat.2013.10
dblp:conf/eusflat/Papco13
fatcat:6r5vdfhmijd77acrgq2nuy7lau
*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. ...##
###
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. ...

##
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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. ...##
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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. ...

##
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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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