Quantum Logics of Fuzzy Representations

Akhilesh Kumar Singh, Rashmi Singh and Bhawna Singh
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Akhilesh Kumar Singh: Department of Applied Sciences and Humanities, Kamla Nehru Institute of Technology, Sultanpur 228118, Uttar Pradesh, India
Rashmi Singh: ��Amity Institute of Applied Sciences, Amity University, Noida 201313, Uttar Pradesh, India
Bhawna Singh: ��Dr. Shyama Prasad Mukherji Government College, Bhadohi 221402, Uttar Pradesh, India

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 03, 1047-1064

Abstract: Quantum logic (QL) and fuzzy logic (FL) have been gaining attention nowadays due to its potential to be used in quantum computing and information theory. This paper aims to provide a comprehensive overview of QL models of fuzzy representations viz. fuzzy sets (FSs), interval valued fuzzy sets (IVFSs), intuitionistic fuzzy sets (IFSs) and interval valued intuitionistic fuzzy sets (IVIFSs). These QL models can be used to analyze the behavior of quantum logical systems in a fuzzy environment, which is particularly useful for dealing with uncertainty and imprecision in quantum environment. Furthermore, this paper explores the concept of effect algebras (EAs), which are algebraic structures that provide a natural framework for studying FL. Specifically, it is shown that the family of FS, IVFS, IFS and IVIFS can be organized into an EA if the Lukasiewicz operations are considered. This result is significant because EAs can be used to model a wide range of physical and mathematical systems, including quantum systems, and provide a useful tool for analyzing the properties of FL.

Keywords: QL; EA; FS; IVFS; IFS; IVIFS (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500504

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