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
In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-filters of a given FI-algebra form a distributive algebraic lattice, par...In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-filters of a given FI-algebra form a distributive algebraic lattice, particularly form a frame.展开更多
A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-L...A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.展开更多
Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft gr...Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.展开更多
In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations betwe...In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations between fuzzy(implicative, associative) filters and falling fuzzy(implicative, associative) filters are provided. In particular, we put forward an open question on a kind of falling fuzzy filters of lattice implication algebras. Finally, we apply falling fuzzy inference relations to lattice implication algebras and obtain some related results.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
The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which...The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.展开更多
In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such...In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters).展开更多
Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equ...Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set,and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices,respectively,based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak’s rough sets and fuzzy rough sets.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.
基金Foundation item： Supported by the National Natural Science Foundation of China（10371106, 60774073）
文摘In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-filters of a given FI-algebra form a distributive algebraic lattice, particularly form a frame.
基金Supported by the National Natural Science Foundation of China(11501523,61673320)。
文摘A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.
文摘Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.
基金Supported by National Natural Science Foundation of China(11461025,61175055)
文摘In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations between fuzzy(implicative, associative) filters and falling fuzzy(implicative, associative) filters are provided. In particular, we put forward an open question on a kind of falling fuzzy filters of lattice implication algebras. Finally, we apply falling fuzzy inference relations to lattice implication algebras and obtain some related results.
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 Higher School Research Foundation of Inner Mongolia(NJSY14283)
文摘The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.
基金Supported by the Graduate Independent Innovation Foundation of Northwest University(YZZ12061)Supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department(2013JK0562)
文摘In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters).
文摘Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set,and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices,respectively,based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak’s rough sets and fuzzy rough sets.
