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Nature of Computation and Communication. 8th EAI International Conference, ICTCC 2022, Vinh Long, Vietnam, October 27-28, 2022, Proceedings

Research Article

Modeling with Words: Steps Towards a Fuzzy Quantum Logic

Cite
BibTeX Plain Text
  • @INPROCEEDINGS{10.1007/978-3-031-28790-9_1,
        author={Nguyen Van Han and Phan Cong Vinh},
        title={Modeling with Words: Steps Towards a Fuzzy Quantum Logic},
        proceedings={Nature of Computation and Communication. 8th EAI International Conference, ICTCC 2022, Vinh Long, Vietnam, October 27-28, 2022, Proceedings},
        proceedings_a={ICTCC},
        year={2023},
        month={3},
        keywords={Linguiatic variable Fuzzy quantum logic Quantum bit},
        doi={10.1007/978-3-031-28790-9_1}
    }
    
  • Nguyen Van Han
    Phan Cong Vinh
    Year: 2023
    Modeling with Words: Steps Towards a Fuzzy Quantum Logic
    ICTCC
    Springer
    DOI: 10.1007/978-3-031-28790-9_1
Nguyen Van Han1, Phan Cong Vinh1,*
  • 1: Faculty of Information Technology, Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Street, Ward 13
*Contact email: pcvinh@ntt.edu.vn

Abstract

On 1936, Birkhoff and von Newmann proposed the introduction of a “quantum logic”, as the lattice of quantum mechanical proposition which is not distributive and also not a Boolean. Seven years later, Mackey tried to provide a set of axioms for the propositional system to predict of the outcome set of experiments. He indicated that the system is an orthocomplemented partially ordered set. Physical complex systems can be modeled by using linguistic variables which are variables whose values may be expressed in terms of a specific natural or artificial language, for example(\mathbb {L})= {very less young; less young; young; more young; very young; very very young ...}. In language of hedge algebra ((\mathbb{H}\mathbb{A})),(\mathbb {L})set which is generated from(\mathbb{H}\mathbb{A})is the POSET (partial order set). In this paper, we introduce a quantum logic(\ell )to assert that, let(\bot )be the orthocomplementation map(\bot : \ell \rightarrow \ell ), all(\clubsuit , \spadesuit \in \bot )must satisfy the following conditions:

((\clubsuit ^\bot )^\bot =\clubsuit )

If(\spadesuit \le \clubsuit )then(\clubsuit ^\bot \le \spadesuit ^\bot )

The greatest lower bound(\clubsuit \vee \clubsuit ^\bot \in \ell )and the least upper bound(\clubsuit \wedge \clubsuit ^\bot \in \ell )

Keywords
Linguiatic variable Fuzzy quantum logic Quantum bit
Published
2023-03-24
Appears in
SpringerLink
http://dx.doi.org/10.1007/978-3-031-28790-9_1
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