A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Second...A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.展开更多
Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain...Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain motion types.The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3).Based on submanifold germs of SE(3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighbor-hood around the identity element of SE(3);two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3).It is also possible to define equivalence relation and partial ordering on the col-lection of parallel mechanisms.In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms.展开更多
This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two ...This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.展开更多
A modified definition of fuzzy transitivity is given.Several properties of this new definition are obtained.Effect of these new properties of transitivity on equivalence relations is also studied.
给出计算偏序集<A,R>的盖住关系的关系矩阵的算法如下:Procedure求哈斯图对应关系阵(MR:n×n偏序关系阵)Q:=MR-I fori:=1ton forj:=1ton fork:=1ton qik:=qik-qik qij qjk end end end{Q=[qij]为Hasse图对应关系}.
文摘A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.
基金supported by the National Basic Research Program of China (2006CB705400)Science & Technology Commission of Shanghai Municipality (071111008)Research & Development Program of China (2006AA4z334)
文摘Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain motion types.The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3).Based on submanifold germs of SE(3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighbor-hood around the identity element of SE(3);two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3).It is also possible to define equivalence relation and partial ordering on the col-lection of parallel mechanisms.In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms.
文摘This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.
文摘A modified definition of fuzzy transitivity is given.Several properties of this new definition are obtained.Effect of these new properties of transitivity on equivalence relations is also studied.
文摘给出计算偏序集<A,R>的盖住关系的关系矩阵的算法如下:Procedure求哈斯图对应关系阵(MR:n×n偏序关系阵)Q:=MR-I fori:=1ton forj:=1ton fork:=1ton qik:=qik-qik qij qjk end end end{Q=[qij]为Hasse图对应关系}.
