In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for...In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of U2, U is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their opimal paradigms ensure the completeness as long as they satisfy some conditions. Finally we consider the problem on the reduction of distributive object sets.展开更多
The article Extension Set and Non-compatible Problems was published in 1983. It proclaimed the birth of extension theory. Its objects of study are contradictory problems in the realistic world; its theoretical pillars...The article Extension Set and Non-compatible Problems was published in 1983. It proclaimed the birth of extension theory. Its objects of study are contradictory problems in the realistic world; its theoretical pillars are matter element theory and extension set theory. Its basic methods are extension methods. Its practical methods are extension engineering methods,展开更多
Invertase （INV） hydrolyzes sucrose into glucose and fructose, thereby playing key roles in primary metabolism and plant development. Based on their pH optima and sub-cellular locations, INVs are categorized into cel...Invertase （INV） hydrolyzes sucrose into glucose and fructose, thereby playing key roles in primary metabolism and plant development. Based on their pH optima and sub-cellular locations, INVs are categorized into cell wall, cytoplasmic, and vacuolar subgroups, abbreviated as CWlN, CIN, and VlN, respectively. The broad importance and implications of INVs in plant development and crop productivity have attracted enormous interest to examine INV function and regulation from multiple perspectives. Here, we review some exciting advances in this area over the last two decades, focusing on （1） new or emerging roles of INV in plant development and regulation at the post-translational level through interaction with inhibitors, （2） cross-talk between INV-mediated sugar signaling and hormonal control of development, and （3） sugar- and INV-mediated responses to drought and heat stresses and their impact on seed and fruit set. Finally, we discuss major questions arising from this new progress and outline future directions for unraveling mechanisms underlying INV-mediated plant development and their potential applications in plant biotechnology and agriculture.展开更多
Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on ...Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on the discernibility matrix (DM),a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction.展开更多
Most traditional assessment methods, which have complicated mathematic formulas, are difficult for calculation and application in water resources system assessment. A new approach to water resources system assessment,...Most traditional assessment methods, which have complicated mathematic formulas, are difficult for calculation and application in water resources system assessment. A new approach to water resources system assessment, the set pair analysis method (SPAM), has been proposed based on the principle of set pair analysis (SPA). The basic ideals and steps of SPAM are discussed. The proposed method can take fuzzy property of threshold values for grade standards into full account and avoid determining the discrepancy uncertainty coefficient i or i1, i2, i3, … in SPA. The presented method is simple in concept, convenient to calculate and feasible for application. Two case studies of water resources assessment have been made. The results show that the proposed method is satisfactory.展开更多
The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to...The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to address the issue of the TE in which the tactic features of the detected target are treated as evaluation attributes. Meanwhile, the intuitionistic fuzzy set （IFS） is employed to deal with information uncertainty in the TE process. Furthermore, on the basis of the entropy weight and inclusion-comparison probability, a hybrid TE method is developed. In order to accommodate the demands of naturalistic decision making, the proposed method allows air defense commanders to express their intuitive opinions besides incorporating into the threat features of the detected target. An illustrative example is provided to indicate the feasibility and advantage of the proposed method.展开更多
Information granulation and entropy theory are two main approaches to research uncertainty of an information system, which have been widely applied in many practical issues. In this paper, the characterizations and re...Information granulation and entropy theory are two main approaches to research uncertainty of an information system, which have been widely applied in many practical issues. In this paper, the characterizations and representations of information granules under various binary relations are investigated in information systems, an axiom definition of information granulation is presented, and some existing definitions of information granulation become its special forms. Entropy theory in information systems is further developed and the granulation monotonicity of each of them is proved. Moreover, the complement relationship between information granulation and entropy is established. This investigation unifies the results of measures for uncertainties in complete information systems and incomplete information systems.展开更多
The definition of the generalized fuzzy set is presented for the first time, and a generalized fuzzy operator is proposed to transform a generalized fuzzy set into a normal fuzzy set. The algorithm theory of the opera...The definition of the generalized fuzzy set is presented for the first time, and a generalized fuzzy operator is proposed to transform a generalized fuzzy set into a normal fuzzy set. The algorithm theory of the operator, as the newest method of the edge detection of a 2-D image, is successfully established. Many experiments haw proved that the algorithm is simpler, more rapid and more precise in location than other edge detection methods. And a schedule of the concrete performance has been given additionally about the edge detection of color images.展开更多
The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized H...The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.展开更多
Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal ...Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in M are determined. The result is proved that for any value s between the maximal and minimal values, there exists an element in M{nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to s. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.展开更多
We give definitions on increasing, constant and decreasing returns to scale under the generalized data envelopment analysis (GDEA) model. The GDEA model prossesses cone structures for describing evaluators’ preferenc...We give definitions on increasing, constant and decreasing returns to scale under the generalized data envelopment analysis (GDEA) model. The GDEA model prossesses cone structures for describing evaluators’ preferences toward different decision making units (DMU) and toward different input / output categories. The GDEA model contains many important DEA models as its subclasses. Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditions for a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, and discuss and clarify the differences and relationships of these conditions under different subclasses of the GDEA model. Furthermore, we describe a method based on a two-stage linear program to test returns to scale properties.展开更多
Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies ...Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov. Our uniform formula can derive a series of the new estimations. Employing the idea of intersection in set theory, we extract a new Leonov formula-like estimation from the family of the estimations. With our method and the new estimation, one can confirm that there are no equilibrium, periodic solutions, almost periodic motions, wandering motions or other chaotic attractors outside the global attractive set. The Lorenz butterfly-like singular attractors are located in the global attractive set only. This result is applied to the chaos control and chaos synchronization. Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution, or globally stabilize an unstable (or locally stable but not globally asymptotically stable) equilibrium. Further, some new global exponential chaos synchronization results are presented. Our new method and the new results are expected to be applied in real secure communication systems.展开更多
文摘In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of U2, U is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their opimal paradigms ensure the completeness as long as they satisfy some conditions. Finally we consider the problem on the reduction of distributive object sets.
文摘The article Extension Set and Non-compatible Problems was published in 1983. It proclaimed the birth of extension theory. Its objects of study are contradictory problems in the realistic world; its theoretical pillars are matter element theory and extension set theory. Its basic methods are extension methods. Its practical methods are extension engineering methods,
文摘Invertase （INV） hydrolyzes sucrose into glucose and fructose, thereby playing key roles in primary metabolism and plant development. Based on their pH optima and sub-cellular locations, INVs are categorized into cell wall, cytoplasmic, and vacuolar subgroups, abbreviated as CWlN, CIN, and VlN, respectively. The broad importance and implications of INVs in plant development and crop productivity have attracted enormous interest to examine INV function and regulation from multiple perspectives. Here, we review some exciting advances in this area over the last two decades, focusing on （1） new or emerging roles of INV in plant development and regulation at the post-translational level through interaction with inhibitors, （2） cross-talk between INV-mediated sugar signaling and hormonal control of development, and （3） sugar- and INV-mediated responses to drought and heat stresses and their impact on seed and fruit set. Finally, we discuss major questions arising from this new progress and outline future directions for unraveling mechanisms underlying INV-mediated plant development and their potential applications in plant biotechnology and agriculture.
文摘Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on the discernibility matrix (DM),a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 50739002, 50779042 and 50679047)
文摘Most traditional assessment methods, which have complicated mathematic formulas, are difficult for calculation and application in water resources system assessment. A new approach to water resources system assessment, the set pair analysis method (SPAM), has been proposed based on the principle of set pair analysis (SPA). The basic ideals and steps of SPAM are discussed. The proposed method can take fuzzy property of threshold values for grade standards into full account and avoid determining the discrepancy uncertainty coefficient i or i1, i2, i3, … in SPA. The presented method is simple in concept, convenient to calculate and feasible for application. Two case studies of water resources assessment have been made. The results show that the proposed method is satisfactory.
基金supported by the National Natural Science Foundation of China (70871117 70571086)the Development Foundation of Dalian Naval Academy
文摘The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to address the issue of the TE in which the tactic features of the detected target are treated as evaluation attributes. Meanwhile, the intuitionistic fuzzy set （IFS） is employed to deal with information uncertainty in the TE process. Furthermore, on the basis of the entropy weight and inclusion-comparison probability, a hybrid TE method is developed. In order to accommodate the demands of naturalistic decision making, the proposed method allows air defense commanders to express their intuitive opinions besides incorporating into the threat features of the detected target. An illustrative example is provided to indicate the feasibility and advantage of the proposed method.
基金the National Natural Science Foundation of China (Grant No.60773133)the National Key Basic Research and Pevelopment Pro-gram of China (973) (Grant No.2007CB311002)the National 863 Project (Grant No.2007AA01Z165)
文摘Information granulation and entropy theory are two main approaches to research uncertainty of an information system, which have been widely applied in many practical issues. In this paper, the characterizations and representations of information granules under various binary relations are investigated in information systems, an axiom definition of information granulation is presented, and some existing definitions of information granulation become its special forms. Entropy theory in information systems is further developed and the granulation monotonicity of each of them is proved. Moreover, the complement relationship between information granulation and entropy is established. This investigation unifies the results of measures for uncertainties in complete information systems and incomplete information systems.
基金the National Natural Science Foundation of China Important Research Foundation of Guangdong Province
文摘The definition of the generalized fuzzy set is presented for the first time, and a generalized fuzzy operator is proposed to transform a generalized fuzzy set into a normal fuzzy set. The algorithm theory of the operator, as the newest method of the edge detection of a 2-D image, is successfully established. Many experiments haw proved that the algorithm is simpler, more rapid and more precise in location than other edge detection methods. And a schedule of the concrete performance has been given additionally about the edge detection of color images.
基金The National Natural Science Foundation of China (No70571087)the National Science Fund for Distinguished Young Scholarsof China (No70625005)
文摘The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.
基金Project supported by the National Climbing Project"Nonlinear Science"and the Scientific Foundation of the State Education Commission of China.
文摘Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in M are determined. The result is proved that for any value s between the maximal and minimal values, there exists an element in M{nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to s. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.
基金This work was supported by the National Natural Science Foundation of China.
文摘We give definitions on increasing, constant and decreasing returns to scale under the generalized data envelopment analysis (GDEA) model. The GDEA model prossesses cone structures for describing evaluators’ preferences toward different decision making units (DMU) and toward different input / output categories. The GDEA model contains many important DEA models as its subclasses. Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditions for a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, and discuss and clarify the differences and relationships of these conditions under different subclasses of the GDEA model. Furthermore, we describe a method based on a two-stage linear program to test returns to scale properties.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.60274007,60474011)the Guangdong Povince Science Foundation for Program of Research Team(Grant No.04205783).
文摘Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov. Our uniform formula can derive a series of the new estimations. Employing the idea of intersection in set theory, we extract a new Leonov formula-like estimation from the family of the estimations. With our method and the new estimation, one can confirm that there are no equilibrium, periodic solutions, almost periodic motions, wandering motions or other chaotic attractors outside the global attractive set. The Lorenz butterfly-like singular attractors are located in the global attractive set only. This result is applied to the chaos control and chaos synchronization. Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution, or globally stabilize an unstable (or locally stable but not globally asymptotically stable) equilibrium. Further, some new global exponential chaos synchronization results are presented. Our new method and the new results are expected to be applied in real secure communication systems.
