As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) ...As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .展开更多
Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their invest...Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .展开更多
In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semi...In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semigroups.展开更多
In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an infor-m...In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an infor-mation system based on binary relation to eliminate limitations of set representation method. Secondly, operators among knowledge granularity are introduced and some important properties of them are studied carefully. Thirdly, distance between two knowledge granules is established and granular space is constructed based on it. Fourthly, axiomatic definition of knowledge granularity is investigated, and one can find that some existed knowledge granularities are special cases under the definition. In addition, as an application of knowledge granular space, an example is employed to validate some results in our work.展开更多
In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for...In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.展开更多
Association rule mining is an important issue in data mining. The paper proposed an binary system based method to generate candidate frequent itemsets and corresponding supporting counts efficiently, which needs only ...Association rule mining is an important issue in data mining. The paper proposed an binary system based method to generate candidate frequent itemsets and corresponding supporting counts efficiently, which needs only some operations such as ＂and＂, ＂or＂ and ＂xor＂. Applying this idea in the existed distributed association rule mining al gorithm FDM, the improved algorithm BFDM is proposed. The theoretical analysis and experiment testify that BFDM is effective and efficient.展开更多
In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of ...In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.展开更多
In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a form...In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a formula for calculate idempotent and regular elements of BX (Q) defined by an X-semilattice of unions D.展开更多
New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it...New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it happens that one has to consider binary relations between the magnitudes having different dimensions. From mathematical point of view, in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems, the binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. The derived structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of Soft Magnetic Composites. This equation constitutes a relation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algorithm for designing the best values of technological parameters.展开更多
In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly r...In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.展开更多
Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation re...Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.展开更多
Protocol Reverse Engineering(PRE)is of great practical importance in Internet security-related fields such as intrusion detection,vulnerability mining,and protocol fuzzing.For unknown binary protocols having fixed-len...Protocol Reverse Engineering(PRE)is of great practical importance in Internet security-related fields such as intrusion detection,vulnerability mining,and protocol fuzzing.For unknown binary protocols having fixed-length fields,and the accurate identification of field boundaries has a great impact on the subsequent analysis and final performance.Hence,this paper proposes a new protocol segmentation method based on Information-theoretic statistical analysis for binary protocols by formulating the field segmentation of unsupervised binary protocols as a probabilistic inference problem and modeling its uncertainty.Specifically,we design four related constructions between entropy changes and protocol field segmentation,introduce random variables,and construct joint probability distributions with traffic sample observations.Probabilistic inference is then performed to identify the possible protocol segmentation points.Extensive trials on nine common public and industrial control protocols show that the proposed method yields higher-quality protocol segmentation results.展开更多
Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered...Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.展开更多
文摘As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .
文摘Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .
文摘In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semigroups.
文摘In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an infor-mation system based on binary relation to eliminate limitations of set representation method. Secondly, operators among knowledge granularity are introduced and some important properties of them are studied carefully. Thirdly, distance between two knowledge granules is established and granular space is constructed based on it. Fourthly, axiomatic definition of knowledge granularity is investigated, and one can find that some existed knowledge granularities are special cases under the definition. In addition, as an application of knowledge granular space, an example is employed to validate some results in our work.
文摘In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.
基金Supported by the National Natural Science Foun-dation of China (70371015)
文摘Association rule mining is an important issue in data mining. The paper proposed an binary system based method to generate candidate frequent itemsets and corresponding supporting counts efficiently, which needs only some operations such as ＂and＂, ＂or＂ and ＂xor＂. Applying this idea in the existed distributed association rule mining al gorithm FDM, the improved algorithm BFDM is proposed. The theoretical analysis and experiment testify that BFDM is effective and efficient.
文摘In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.
文摘In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a formula for calculate idempotent and regular elements of BX (Q) defined by an X-semilattice of unions D.
基金supported by National Center of Science within the framework of research project Grant N N507 249940.
文摘New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it happens that one has to consider binary relations between the magnitudes having different dimensions. From mathematical point of view, in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems, the binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. The derived structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of Soft Magnetic Composites. This equation constitutes a relation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algorithm for designing the best values of technological parameters.
基金Supported by the National Natural Science Foundation of China(10861007)
文摘In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.
文摘Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.
文摘Protocol Reverse Engineering(PRE)is of great practical importance in Internet security-related fields such as intrusion detection,vulnerability mining,and protocol fuzzing.For unknown binary protocols having fixed-length fields,and the accurate identification of field boundaries has a great impact on the subsequent analysis and final performance.Hence,this paper proposes a new protocol segmentation method based on Information-theoretic statistical analysis for binary protocols by formulating the field segmentation of unsupervised binary protocols as a probabilistic inference problem and modeling its uncertainty.Specifically,we design four related constructions between entropy changes and protocol field segmentation,introduce random variables,and construct joint probability distributions with traffic sample observations.Probabilistic inference is then performed to identify the possible protocol segmentation points.Extensive trials on nine common public and industrial control protocols show that the proposed method yields higher-quality protocol segmentation results.
文摘Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.
