In the paper,we introduce some of multipliers on residuated lattices and investigate the relations among them.First,basing on the properties of multipliers,we show that the set of all multiplicative multipliers on a r...In the paper,we introduce some of multipliers on residuated lattices and investigate the relations among them.First,basing on the properties of multipliers,we show that the set of all multiplicative multipliers on a residuated lattice A forms a residuated lattice which is isomorphic to A.Second,we prove that the set of all total multipliers on A is a Boolean subalgebra of the residuated lattice(which is constituted by all multiplicative multipliers on A)and is isomorphic to the Boolean center of A.Moreover,by partial multipliers,we study the maximal residuated lattices of quotients for residuated lattices.Finally,we focus on principal implicative multipliers on residuated lattices and obtain that the set of principal implicative multipliers on A is isomorphic to the set of all multiplicative multipliers on A under the opposite(dual)order.展开更多
This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice....This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.展开更多
In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
This paper is devoted to the discussion of filters in residuated lattices. Some equivalent conditions about filter were given. The structure of generated filter was established. The concept of implicative filter in re...This paper is devoted to the discussion of filters in residuated lattices. Some equivalent conditions about filter were given. The structure of generated filter was established. The concept of implicative filter in residuated lattice was proposed with its basic properties being discussed.展开更多
Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems....Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.展开更多
Transition metal chalcogenides(TMCs)are recognized as pre-catalysts,and their(oxy)hydroxides derived from electrochemical reconstruction are the active species in the water oxidation.However,understanding the role of ...Transition metal chalcogenides(TMCs)are recognized as pre-catalysts,and their(oxy)hydroxides derived from electrochemical reconstruction are the active species in the water oxidation.However,understanding the role of the residual chalcogen in the reconstructed layer is lacking in detail,and the corresponding catalytic mechanism remains controversial.Here,taking Cu_(1-x)Co_(x)S as a platform,we explore the regulating effect and existence form of the residual S doped into the reconstructive layer for oxygen evolution reaction(OER),where a dual-path OER mechanism is proposed.First-principles calculations and operando~(18)O isotopic labeling experiments jointly reveal that the residual S in the reconstructive layer of Cu_(1-x)Co_(x)S can wisely balance the adsorbate evolution mechanism(AEM)and lattice oxygen oxidation mechanism(LOM)by activating lattice oxygen and optimizing the adsorption/desorption behaviors at metal active sites,rather than change the reaction mechanism from AEM to LOM.Following such a dual-path OER mechanism,Cu_(0.4)Co_(0.6)S-derived Cu_(0.4)Co_(0.6)OSH not only overcomes the restriction of linear scaling relationship in AEM,but also avoids the structural collapse caused by lattice oxygen migration in LOM,so as to greatly reduce the OER potential and improved stability.展开更多
We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
We give two generalizations of Tarski’s fixpoint theorem in the setting of residuated lattices and use them to establish van Emdem-Kowalski’s least fixpoint semantics for residuated lattice-valued logic programs.
基金supported by the National Natural Science Foundation of China(11531009).
文摘In the paper,we introduce some of multipliers on residuated lattices and investigate the relations among them.First,basing on the properties of multipliers,we show that the set of all multiplicative multipliers on a residuated lattice A forms a residuated lattice which is isomorphic to A.Second,we prove that the set of all total multipliers on A is a Boolean subalgebra of the residuated lattice(which is constituted by all multiplicative multipliers on A)and is isomorphic to the Boolean center of A.Moreover,by partial multipliers,we study the maximal residuated lattices of quotients for residuated lattices.Finally,we focus on principal implicative multipliers on residuated lattices and obtain that the set of principal implicative multipliers on A is isomorphic to the set of all multiplicative multipliers on A under the opposite(dual)order.
文摘This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.
文摘In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
文摘This paper is devoted to the discussion of filters in residuated lattices. Some equivalent conditions about filter were given. The structure of generated filter was established. The concept of implicative filter in residuated lattice was proposed with its basic properties being discussed.
基金The National Natural Science Foundation of China (No60474022)
文摘Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.
基金supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202200550)the Natural Science Foundation Joint Fund for Innovation and Development of Chongqing Municipal Education Commission(CSTB2022NSCQ-LZX0077)+4 种基金the National Natural Science Foundation of China(No.52100065)the Science and Technology Research Program of Natural Science Foundation of Chongqing(cstc2021ycjh-bgzxm0037)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-M202200503)the Chongqing Innovation Research Group Project(No.CXQT21015)the Doctor Start/Talent Introduction Program of Chongqing Normal University(No.02060404/2020009000321)。
文摘Transition metal chalcogenides(TMCs)are recognized as pre-catalysts,and their(oxy)hydroxides derived from electrochemical reconstruction are the active species in the water oxidation.However,understanding the role of the residual chalcogen in the reconstructed layer is lacking in detail,and the corresponding catalytic mechanism remains controversial.Here,taking Cu_(1-x)Co_(x)S as a platform,we explore the regulating effect and existence form of the residual S doped into the reconstructive layer for oxygen evolution reaction(OER),where a dual-path OER mechanism is proposed.First-principles calculations and operando~(18)O isotopic labeling experiments jointly reveal that the residual S in the reconstructive layer of Cu_(1-x)Co_(x)S can wisely balance the adsorbate evolution mechanism(AEM)and lattice oxygen oxidation mechanism(LOM)by activating lattice oxygen and optimizing the adsorption/desorption behaviors at metal active sites,rather than change the reaction mechanism from AEM to LOM.Following such a dual-path OER mechanism,Cu_(0.4)Co_(0.6)S-derived Cu_(0.4)Co_(0.6)OSH not only overcomes the restriction of linear scaling relationship in AEM,but also avoids the structural collapse caused by lattice oxygen migration in LOM,so as to greatly reduce the OER potential and improved stability.
基金supported by the National Foundation for Distionguished Young Scholars(Grant No:69725004)Rrsearch and Development Project of High-Technology(Grant No:863-306-ZT06-04-3)+1 种基金Foundation of Natural Sciences(Grant No:6982001) of ChinaFOK Ying-Tung Edu
文摘We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
文摘We give two generalizations of Tarski’s fixpoint theorem in the setting of residuated lattices and use them to establish van Emdem-Kowalski’s least fixpoint semantics for residuated lattice-valued logic programs.
