In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal...In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.展开更多
We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prov...We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prove the adjoint semigroup of a bounded implicative BCK algebra is a Boolean algebra.展开更多
Parkinson's disease is a neurodegenerative disorder marked by the degeneration of dopaminergic neurons and clinical symptoms such as tremors,rigidity,and slowed movements.A key feature of Parkinson's disease i...Parkinson's disease is a neurodegenerative disorder marked by the degeneration of dopaminergic neurons and clinical symptoms such as tremors,rigidity,and slowed movements.A key feature of Parkinson's disease is the accumulation of misfoldedα-synuclein,forming insoluble Lewy bodies in the substantia nigra pars compacta,which contributes to neurodegeneration.Theseα-synuclein aggregates may act as autoantigens,leading to T-cell-mediated neuroinflammation and contributing to dopaminergic cell death.Our perspective explores the hypothesis that Parkinson's disease may have an autoimmune component,highlighting research that connects peripheral immune responses with neurodegeneration.T cells derived from Parkinson's disease patients appear to have the potential to initiate an autoimmune response againstα-synuclein and its modified peptides,possibly leading to the formation of neo-epitopes.Recent evidence associates Parkinson's disease with abnormal immune responses,as indicated by increased levels of immune cells,such as CD4^(+)and CD8^(+)T cells,observed in both patients and mouse models.The convergence of T cells filtration increasing major histocompatibility complex molecules,and the susceptibility of dopaminergic neurons supports the hypothesis that Parkinson's disease may exhibit autoimmune characteristics.Understanding the immune mechanisms involved in Parkinson's disease will be crucial for developing therapeutic strategies that target the autoimmune aspects of the disease.Novel approaches,including precision medicine based on major histocompatibility complex/human leukocyte antigen typing and early biomarker identification,could pave the way for immune-based treatments aimed at slowing or halting disease progression.This perspective explores the relationship between autoimmunity and Parkinson's disease,suggesting that further research could deepen understanding and offer new therapeutic avenues.In this paper,it is organized to provide a comprehensive perspective on the autoimmune aspects of Parkinson's disease.It investigates critical areas such as the autoimmune response observed in Parkinson's disease patients and the role of autoimmune mechanisms targetingα-synuclein in Parkinson's disease.The paper also examines the impact of CD4~+T cells,specifically Th1 and Th17,on neurons through in vitro and ex vivo studies.Additionally,it explores howα-synuclein influences glia-induced neuroinflammation in Parkinson's disease.The discussion extends to the clinical implications and therapeutic landscape,offering insights into potential treatments.Consequently,we aim to provide a comprehensive perspective on the autoimmune aspects of Parkinson's disease,incorporating both supportive and opposing views on its classification as an autoimmune disorder and exploring implications for clinical applications.展开更多
The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuati...The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuation and an implicative pseudo valuation and obtain some characterizations of implicative pseudo valuations. In particular, we show that a pseudo valuation on regular hoops is implicative if and only if it satisfies φ(x■x') = 0.This result will provide a more general algebraic foundation for pseudo valuations theory on algebraic structures based on substructure logic.展开更多
Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the...Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.展开更多
In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary ...In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.展开更多
We introduce the notions of implicative ideals and fuzzy implicative ideals of a distributive implication groupoid. Some properties of these ideals will be investigated. In particular, the necessary and sufficient con...We introduce the notions of implicative ideals and fuzzy implicative ideals of a distributive implication groupoid. Some properties of these ideals will be investigated. In particular, the necessary and sufficient conditions for an ideal（fuzzy ideal） to be an implicative ideal（fuzzy implicative ideal） is given. By using the concept of level sets, we will characterize the fuzzy implicative ideals of a distributive implication groupoid. Finally, an extension property for fuzzy implicative ideals is given.展开更多
文摘In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.
文摘We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prove the adjoint semigroup of a bounded implicative BCK algebra is a Boolean algebra.
基金supported by the National Research Foundation of South Korea(2023R1A2C2004516,RS-2023-00219399 to SPY,and 2022R1I1A1A01063513 to MGJ)。
文摘Parkinson's disease is a neurodegenerative disorder marked by the degeneration of dopaminergic neurons and clinical symptoms such as tremors,rigidity,and slowed movements.A key feature of Parkinson's disease is the accumulation of misfoldedα-synuclein,forming insoluble Lewy bodies in the substantia nigra pars compacta,which contributes to neurodegeneration.Theseα-synuclein aggregates may act as autoantigens,leading to T-cell-mediated neuroinflammation and contributing to dopaminergic cell death.Our perspective explores the hypothesis that Parkinson's disease may have an autoimmune component,highlighting research that connects peripheral immune responses with neurodegeneration.T cells derived from Parkinson's disease patients appear to have the potential to initiate an autoimmune response againstα-synuclein and its modified peptides,possibly leading to the formation of neo-epitopes.Recent evidence associates Parkinson's disease with abnormal immune responses,as indicated by increased levels of immune cells,such as CD4^(+)and CD8^(+)T cells,observed in both patients and mouse models.The convergence of T cells filtration increasing major histocompatibility complex molecules,and the susceptibility of dopaminergic neurons supports the hypothesis that Parkinson's disease may exhibit autoimmune characteristics.Understanding the immune mechanisms involved in Parkinson's disease will be crucial for developing therapeutic strategies that target the autoimmune aspects of the disease.Novel approaches,including precision medicine based on major histocompatibility complex/human leukocyte antigen typing and early biomarker identification,could pave the way for immune-based treatments aimed at slowing or halting disease progression.This perspective explores the relationship between autoimmunity and Parkinson's disease,suggesting that further research could deepen understanding and offer new therapeutic avenues.In this paper,it is organized to provide a comprehensive perspective on the autoimmune aspects of Parkinson's disease.It investigates critical areas such as the autoimmune response observed in Parkinson's disease patients and the role of autoimmune mechanisms targetingα-synuclein in Parkinson's disease.The paper also examines the impact of CD4~+T cells,specifically Th1 and Th17,on neurons through in vitro and ex vivo studies.Additionally,it explores howα-synuclein influences glia-induced neuroinflammation in Parkinson's disease.The discussion extends to the clinical implications and therapeutic landscape,offering insights into potential treatments.Consequently,we aim to provide a comprehensive perspective on the autoimmune aspects of Parkinson's disease,incorporating both supportive and opposing views on its classification as an autoimmune disorder and exploring implications for clinical applications.
基金Supported by a grant of National Natural Science Foundation of China（11571281）
文摘The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuation and an implicative pseudo valuation and obtain some characterizations of implicative pseudo valuations. In particular, we show that a pseudo valuation on regular hoops is implicative if and only if it satisfies φ(x■x') = 0.This result will provide a more general algebraic foundation for pseudo valuations theory on algebraic structures based on substructure logic.
文摘Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.
文摘In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.
文摘We introduce the notions of implicative ideals and fuzzy implicative ideals of a distributive implication groupoid. Some properties of these ideals will be investigated. In particular, the necessary and sufficient conditions for an ideal（fuzzy ideal） to be an implicative ideal（fuzzy implicative ideal） is given. By using the concept of level sets, we will characterize the fuzzy implicative ideals of a distributive implication groupoid. Finally, an extension property for fuzzy implicative ideals is given.
