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• W4313894088 abstract "This paper reveals some relations between fuzzy logic and quantum logic on partial residuated implications (PRIs) induced by partial t-norms as well as proposes partial residuated monoids (PRMs) and partial residuated lattices (PRLs) by defining partial adjoint pairs. First of all, we introduce the connection between lattice effect algebra and partial t-norms according to the concept of partial t-norms given by Borzooei, together with the proof that partial operation in any commutative quasiresiduated lattice is partial t-norm. Then, we offer the general form of PRI and the definition of partial fuzzy implication (PFI), give the condition that partial residuated implication is a fuzzy implication, and prove that each PRI is a PFI. Next, we propose PRLs, study their basic characteristics, discuss the correspondence between PRLs and lattice effect algebras (LEAs), and point out the relationship between LEAs and residuated partial algebras. In addition, like the definition of partial t-norms, we provide the notions of partial triangular conorms (partial t-conorms) and corresponding partial co-residuated lattices (PcRLs). Lastly, based on partial residuated lattices, we define well partial residuated lattices (wPRLs), study the filter of well partial residuated lattices, and then construct quotient structure of PRMs." @default.
• W4313894088 created "2023-01-10" @default.
• W4313894088 creator A5008199212 @default.
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• W4313894088 date "2023-01-06" @default.
• W4313894088 modified "2023-10-14" @default.
• W4313894088 title "Partial Residuated Implications Induced by Partial Triangular Norms and Partial Residuated Lattices" @default.
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• W4313894088 doi "https://doi.org/10.3390/axioms12010063" @default.
• W4313894088 hasPublicationYear "2023" @default.
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