Regular Partial Residuated Lattices and Their Filters

Nan Sheng and Xiaohong Zhang
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Nan Sheng: School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China
Xiaohong Zhang: School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China

Mathematics, 2022, vol. 10, issue 14, 1-16

Abstract: To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices.

Keywords: fuzzy logic; partial t-norm; regular partial residuated lattice; Q-residuated lattice; filter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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