We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph model...We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.展开更多
In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem ar...In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem are obtained.展开更多
针对粒度支持向量机进行粒划分后提取代表点时丢失部分重要分类信息从而影响分类准确率的情况,提出了一种基于近邻边界的粒度支持向量机(Neighboring-boundary Granular Support Vector Machine,NGSVM)的学习策略。首先采用kmeans方法...针对粒度支持向量机进行粒划分后提取代表点时丢失部分重要分类信息从而影响分类准确率的情况,提出了一种基于近邻边界的粒度支持向量机(Neighboring-boundary Granular Support Vector Machine,NGSVM)的学习策略。首先采用kmeans方法进行粒划分,对不同的粒依据不同的规则提取粒内代表点,并按照要求分别将代表点放入精简集或修正集中,再用这两个集合中的数据对支持向量机进行训练;形成分类器后,根据核空间距离提取靠近分类面的近邻边界数据以对分类面进行修正。仿真实验结果表明,通过提取靠近分类面的近邻边界数据进行重新训练,能够修正分类面,进一步提高粒度支持向量机的分类准确率。展开更多
This paper focuses on fixed-interval smoothing for stochastic hybrid systems.When the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance de...This paper focuses on fixed-interval smoothing for stochastic hybrid systems.When the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable.We develop a fixedinterval smoothing method based on forward-and backward-filtering in the Variable Structure Multiple Model(VSMM)framework in this paper.We propose to use the Simplified Equivalent model Interacting Multiple Model(SEIMM)in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters,and design a re-filtering procedure in the model-switching stage to enhance the estimation performance.To improve the computational efficiency,we make the basic model-set adaptive by the Likely-Model Set(LMS)algorithm.It turns out that the smoothing performance is further improved by the LMS due to less competition among models.Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.展开更多
In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations an...In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].展开更多
In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of <em>non-surjective injective</em> maps. The non-surjective injective maps from an infinite...In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of <em>non-surjective injective</em> maps. The non-surjective injective maps from an infinite set to itself constitute a semigroup for the <em>law of composition</em> bundled with certain properties allowing us to prove the existence of remarkable elements. Not to mention a compatible equivalence relation that allows transferring the <em>said law</em> to the quotient set, which can be provided with a lattice structure. Finally, we will present the concept of <em>Co-injectivity</em> and some of its properties.展开更多
In the present paper, we define Dislocated Soft Metric Space and discuss about the existence and uniqueness of soft fixed point of a cyclic mapping in soft dislocated metric space. We also prove the unique soft fixed ...In the present paper, we define Dislocated Soft Metric Space and discuss about the existence and uniqueness of soft fixed point of a cyclic mapping in soft dislocated metric space. We also prove the unique soft fixed point theorems of a cyclic mapping in the context of dislocated soft metric space. Examples are given for support of the results.展开更多
The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point ...The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point theorem is equivalent to the generalized Ekeland variational principle.展开更多
This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Ca...This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].展开更多
文摘We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.
基金Supported by the Scientific Research Foundation of Bijie University(20072001)
文摘In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem are obtained.
文摘针对粒度支持向量机进行粒划分后提取代表点时丢失部分重要分类信息从而影响分类准确率的情况,提出了一种基于近邻边界的粒度支持向量机(Neighboring-boundary Granular Support Vector Machine,NGSVM)的学习策略。首先采用kmeans方法进行粒划分,对不同的粒依据不同的规则提取粒内代表点,并按照要求分别将代表点放入精简集或修正集中,再用这两个集合中的数据对支持向量机进行训练;形成分类器后,根据核空间距离提取靠近分类面的近邻边界数据以对分类面进行修正。仿真实验结果表明,通过提取靠近分类面的近邻边界数据进行重新训练,能够修正分类面,进一步提高粒度支持向量机的分类准确率。
基金supported in part by the National Natural Science Foundation of China(No.61773306)the National Key Research and Development Plan,China(Nos.2021YFC2202600 and 2021YFC2202603)。
文摘This paper focuses on fixed-interval smoothing for stochastic hybrid systems.When the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable.We develop a fixedinterval smoothing method based on forward-and backward-filtering in the Variable Structure Multiple Model(VSMM)framework in this paper.We propose to use the Simplified Equivalent model Interacting Multiple Model(SEIMM)in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters,and design a re-filtering procedure in the model-switching stage to enhance the estimation performance.To improve the computational efficiency,we make the basic model-set adaptive by the Likely-Model Set(LMS)algorithm.It turns out that the smoothing performance is further improved by the LMS due to less competition among models.Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.
基金Supported by a grant of National Natural Science Foundation of China(12001243,61976244,12171294,11961016)the Natural Science Basic Research Plan in Shaanxi Province of China(2020JQ-762,2021JQ-580)。
文摘In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].
文摘In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of <em>non-surjective injective</em> maps. The non-surjective injective maps from an infinite set to itself constitute a semigroup for the <em>law of composition</em> bundled with certain properties allowing us to prove the existence of remarkable elements. Not to mention a compatible equivalence relation that allows transferring the <em>said law</em> to the quotient set, which can be provided with a lattice structure. Finally, we will present the concept of <em>Co-injectivity</em> and some of its properties.
文摘In the present paper, we define Dislocated Soft Metric Space and discuss about the existence and uniqueness of soft fixed point of a cyclic mapping in soft dislocated metric space. We also prove the unique soft fixed point theorems of a cyclic mapping in the context of dislocated soft metric space. Examples are given for support of the results.
基金Tianyuan Young Mathematics of China under Grant (10526025)Science Foundation of Nanjing Normal University under Grant(2002SXXXGQ2B20)
文摘The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point theorem is equivalent to the generalized Ekeland variational principle.
文摘This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].
