14 results on '"Wen, Ching-Feng"'
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2. Algebraic formulae for solving systems of max-min inverse fuzzy relational equations.
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Wen, Ching-Feng, Wu, Yan-Kuen, and Li, Zhaowen
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FUZZY relational equations , *EXPERT systems , *GROUP decision making - Abstract
This article is intended to solve the systems of inverse fuzzy relational equations with max–min composition, which is beneficial for solving the well-known problems of fuzzy abductive/backward reasoning. Almost all the existing methods are based on numerical algorithms, and either cannot find the globally optimal solutions or consume significant computational cost to acquire the most accurate result. Due to these drawbacks, the existing methods seem not to render the retroduction applying inverse fuzzy relation popular in many real-time expert systems such as intelligent diagnosis. It is well known that the system of inverse fuzzy relational equations is not always consistent. In this case, according to the preselected weights, we employ weighted L 1 norm distances to define a variety of best approximate solutions. Then we show that there exist very straightforward algebraic formulae for finding the best approximate solutions. The proposed approach not only finds the globally optimal solutions, but also has the advantage of being computationally very simple and efficient, and hence it has a lot of potentials to perform real-time abductive reasoning in many expert systems. [ABSTRACT FROM AUTHOR]
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- 2023
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3. Fixed points of functions with max-weighted quasi-arithmetic mean operator.
- Author
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Wen, Ching-Feng, Liu, Chia-Cheng, and Lur, Yung-Yih
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FIXED point theory , *ARITHMETIC mean , *OPERATOR theory , *CONTINUOUS functions , *MONOTONE operators , *MATRICES (Mathematics) , *MATHEMATICAL sequences - Abstract
Abstract: Let and f be a continuous, strictly monotone real-valued function. The weighted quasi-arithmetic mean of two numbers a, b is defined by . Let be an real matrix and . We construct a function by for all . In this paper we show that has a unique fixed point . Moreover, it can be shown that for each the sequence , generated by the following iterative scheme: and for all , converges to the unique fixed point . Besides, some properties of the fixed point are derived. As an application, our results imply that the max-weighted quasi-arithmetic mean powers of any matrix are always convergent. The continuity of the function defined by is proposed as well. [Copyright &y& Elsevier]
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- 2014
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4. On a recurrence algorithm for continuous-time linear fractional programming problems
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Wen, Ching-Feng, Lur, Yung-Yih, Guu, Sy-Ming, and Stanley Lee, E.
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RECURSIVE sequences (Mathematics) , *ALGORITHMS , *FRACTIONAL calculus , *LINEAR programming , *APPROXIMATION theory , *STATISTICAL decision making , *STOCHASTIC convergence - Abstract
Abstract: In this paper, we develop a discrete approximation method for solving continuous-time linear fractional programming problems. Our method enables one to derive a recurrence structure which shall overcome the computational curse caused by the increasing numbers of decision variables in the approximate decision problems when the subintervals are getting smaller and smaller. Furthermore, our algorithm provides estimation for the error bounds of the approximate solutions. We also establish the convergence of our approximate solutions to the continuous-time linear fractional programming problems. Numerical examples are provided to illustrate the quality of the approximate solutions. [Copyright &y& Elsevier]
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- 2010
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5. Approximate controllability for fractional semilinear parabolic equations.
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Huang, Yong, Liu, Zhenhai, and Wen, Ching-Feng
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PARABOLIC operators , *FRACTIONAL differential equations , *CONTROLLABILITY in systems engineering , *LINEAR operators , *EQUATIONS , *NONLINEAR analysis - Abstract
In this paper, we deal with the control systems described by a large class of fractional semilinear parabolic equations. Firstly, we reformulate the fractional parabolic equations into abstract fractional differential equations associated with a semigroup on an appropriate Banach space. Secondly, we introduce a suitable concept on a mild solution for this kind of fractional parabolic equations and present the existence and uniqueness of mild solution by utilizing the theory of semigroup of linear operator, nonlinear analysis method and fixed point theorem. Then, the approximate controllability of the fractional semilinear parabolic equations is formulated and proved. At the end of the paper, an example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]
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- 2019
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6. Gaussian kernel based gene selection in a single cell gene decision space.
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Li, Zhaowen, Feng, Junhong, Zhang, Jie, Liu, Fang, Wang, Pei, and Wen, Ching-Feng
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ENTROPY (Information theory) , *REAL numbers , *GENE expression , *GENES , *INFORMATION storage & retrieval systems - Abstract
Information system is a database that shows relationships between objects and attributes. A real-valued information system is an information system whose information values are real numbers. A real-valued information system with decision attributes is referred to as a real-valued decision information system. If objects, conditional attributes and information values in a real-valued decision information system are cells, genes and gene expression values, respectively, then this information system is said to be a gene decision space. In a gene decision space, people are faced with gene expression data. If gene expression data in a gene decision space changes to single cell RNA-seq data, then this space is referred to as a single cell gene decision space. This paper explores gene selection in a single cell gene decision space in terms of Gaussian kernel. In the first place, the distance between two cells in each subspace of a single cell gene decision space is constructed. Next, the fuzzy T cos -equivalence relation on the cell set is obtained in terms of Gaussian kernel. After that, measures of uncertainty for a single cell gene decision space are investigated. Lastly, gene selection algorithms in a single cell gene decision space are presented in terms of the proposed information entropy and information granularity. The presented algorithms are testified in several publicly open single cell RNA-seq data sets. Experimental results reveal that the presented algorithms can select appropriate genes related to classification, and significantly improve classification performances. [ABSTRACT FROM AUTHOR]
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- 2022
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7. On general systems of variational inequalities.
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Ceng, Lu-Chuan, Kong, Zhao-Rong, and Wen, Ching-Feng
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VARIATIONAL inequalities (Mathematics) , *MATHEMATICAL proofs , *VISCOSITY , *APPROXIMATION theory , *STOCHASTIC convergence , *FIXED point theory - Abstract
Abstract: In this paper, we present a new relaxed viscosity approximation method, and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a suitable equilibrium problem and a general system of variational inequalities. [Copyright &y& Elsevier]
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- 2013
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8. Uncertainty measurement for single cell RNA-seq data via Gaussian kernel: Application to unsupervised gene selection.
- Author
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Li, Zhaowen, Zhang, Jie, Liu, Fang, and Wen, Ching-Feng
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RNA sequencing , *REAL numbers , *ENTROPY (Information theory) , *GENE expression , *GENES , *FEATURE selection - Abstract
A real-valued information system (RVIS) is an information system (IS) whose information values are real numbers. If the objects, attributes and information values of a RVIS change to cells, genes and gene expression values where gene expression data is single cell RNA-seq (scRNA) data, respectively, then this RVIS is referred to as a single cell gene space (s c g -space). Unsupervised gene selection becomes very challenging due to a lack of decision information, which is to select the optimal gene subset that can maintain learning ability without decision information. However, little research has been done on unsupervised gene selection. Uncertainty measurement is a tool of gene selection. In view of this, this paper studies uncertainty measurement in an s c g -space via Gaussian kernel and explores its application for unsupervised gene selection. In the first place, the distance between two cells in a given subspace is constructed. In the next place, the fuzzy T c o s -equivalence relation induced by this subspace is obtained employing Gaussian kernel. After that, measures of uncertainty for an s c g -space are investigated. Lastly, gene selection algorithms in an s c g -space are presented by using the proposed information entropy and information granularity. The presented algorithms are applied to clustering analyses of scRNA data. Multiple publicly available scRNA data sets are employed to evaluate the gene selection performances of the presented algorithms, while two commonly-used clustering methods, kmeans and AGNES, are utilized to obtain four metrics such as Silhouette Coefficient (S C), Davies–Bouldin Index (D B I), Fowlkes and Mallows Index (F M I), Normalized Mutual Information (N M I). The clustering results demonstrated that the presented algorithms can lower significantly the number genes selected, achieve the better S C , D B I , F M I and N M I. They also show that the presented algorithms are superior to raw data and PCA and NMF regardless of using kmeans or AGNES clustering. This also indirectly demonstrates that the granulation measure and information entropy can effectively evaluate the uncertainty of an s c g -space. [ABSTRACT FROM AUTHOR]
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- 2024
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9. Feature selection for multi-labeled data based on label enhancement technique and mutual information.
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Zhang, Qinli, Liu, Suping, Wang, Jun, Li, Zhaowen, and Wen, Ching-Feng
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FEATURE selection , *ALGORITHMS - Abstract
In multi-label data, the importance of each label within the logical label vector varies for each sample, and there exist inherent correlations among the labels. However, the logical label vector fails to capture these nuances. Consequently, relying solely on this vector for feature selection in multi-label data results in underutilization of supervisory information. To address this issue, this paper introduces a novel label enhancement algorithm. This algorithm leverages neighborhood information derived from features to transform the logical label vector into a label distribution that effectively reflects label differences and correlations. Subsequently, we propose a feature selection algorithm tailored for multi-label data, which incorporates both the transformed label distribution and mutual information. This algorithm not only accounts for the mutual information between features and label distributions but also captures the mutual information among features themselves. Finally, we evaluate our proposed feature selection algorithm against five state-of-the-art multi-label feature selection algorithms on ten publicly available datasets. The experimental results reveal that our algorithm outperforms its competitors in six distinct evaluation metrics, achieving an average performance improvement of approximately 9%. This substantial enhancement underscores the efficacy of our algorithm in handling complex multi-label data. [ABSTRACT FROM AUTHOR]
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- 2024
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10. New uncertainty measurement for hybrid data and its application in attribute reduction.
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Huang, Haixin, Li, Zhaowen, Liu, Fang, and Wen, Ching-Feng
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ROUGH sets , *ENTROPY (Information theory) , *STATISTICS , *INFORMATION storage & retrieval systems , *DATA distribution , *QUANTUM information theory - Abstract
Due to limitations in data acquisition, data in real life often contains a wealth of uncertain information. Uncertainty measurement (UM) constructed within the framework of rough set theory (RST) is an important tool for processing uncertain information. Some basic UMs in RST such as classification precision, rough membership degree, dependence degree, and attribute importance cannot accurately measure the uncertainty of a hybrid information system (HIS). For example, dependence degree only considers the information provided by the lower approximation of the decision and ignores the upper approximation, which may lead to some information loss. In addition to these basic UMs, some extended entropy-based UMs such as rough entropy, information entropy and conditional entropy are also frequently used to measure the uncertainty of a HIS. However, these three UMs also have their own drawbacks. For instance, rough entropy is sensitive to the distribution of hybrid data. When the distribution of hybrid data is uneven, the calculation results of rough entropy may be greatly affected, leading to a decrease in measurement accuracy. This paper proposes four new UMs in a HIS and provides an application in attribute reduction. First of all, a distance function is defined to deal with each type of attribute in a HIS and construct a tolerance relation. On this basis, four UMs are listed to measure the uncertainty of a HIS. Next, the strength and weakness of the proposed UMs are verified by statistical analysis. Subsequently, the UM with the best performance is selected to design an attribute reduction algorithm. Finally, the designed algorithm is compared with other five attribute reduction algorithms to show its superior performance. [ABSTRACT FROM AUTHOR]
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- 2024
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11. A novel method to information fusion in multi-source incomplete interval-valued data via conditional information entropy: Application to mutual information entropy based attribute reduction.
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Li, Zhaowen, Liu, Jianming, Peng, Yichun, and Wen, Ching-Feng
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ENTROPY (Information theory) , *MISSING data (Statistics) , *HUFFMAN codes , *INFORMATION resources - Abstract
In the era of explosive data growth, data sources and volumes are rapidly increasing. A multi-source data refers to information from multi-sources. However, not every source of information is equally important; some sources are more important and some are essentially worthless. Therefore, it is very meaningful to study how to select the most valuable sources and to efficiently fuse information. Multi-source incomplete interval-valued data (MSIIV-data) is an important kind of multi-source data. This paper proposes a novel method to information fusion in MSIIV-data via conditional information entropy (CIE) and considers its application to attribute reduction based on mutual information entropy. First, the distance between two information values for each incomplete interval-valued data is defined, the neighborhood classes with a tunable parameter are obtained, and the neighborhood granularity structure is established. Then, a source selection method is given via CIE, which is used to fuse MSIIV-data into single-source incomplete interval-valued data (SSIIV-data). Based on the minimization of CIE, this method allows worthy and reliable information sources to be chosen. Moreover, an attribute reduction algorithm (denoted as MMQPSO) for the fused SSIIV-data is proposed by means of combining mutual information entropy and QPSO-algorithm. Finally, experiments are done to validate the effectiveness of the proposed algorithms. The results of experiment and statistical test on 12 datasets show that the proposed algorithms have certain feasibility and advancement than 6 other advanced algorithms. [ABSTRACT FROM AUTHOR]
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- 2024
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12. New uncertainty measurement for categorical data based on fuzzy information structures: An application in attribute reduction.
- Author
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Zhang, Qinli, Chen, Yiying, Zhang, Gangqiang, Li, Zhaowen, Chen, Lijun, and Wen, Ching-Feng
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GROUP decision making , *ROUGH sets , *ENTROPY (Information theory) - Abstract
Categorical data is a significant kind of data in machine learning.Generally, rough set theory (RS -theory) deals with categorical data in the following way.First, an equivalence relation based on the equality of attribute values of categorical data is established.Then, information granules (I -granules) based on equivalence classes are obtained.Finally, information structures (I -structures) consisting of I -granules are formed.However, an equivalence relation is too strict, and there are some limitations in the I -structure of a categorical information system (CIS) that may result in filtering out potentially useful information.This paper investigates fuzzy information structures (FI -structures) and new uncertainty measurements for categorical data from the perspective that "the equality of attribute values is fed back to the attribute set".First, a fuzzy symmetry relation based on the number of attributes with equal attribute values is established. Then, fuzzy information granules (FI -granules) based on the fuzzy symmetry relation are obtained. Next, FI -structures consisting of FI -granules are formed.Finally, some concepts related to FI -structures in a CIS are given.The set vector is used to denote FI -structures, and the inclusion degree is used to study the dependence between FI -structures.In addition, four new uncertainty measurements based on FI -structures in a CIS are proposed, including fuzzy information granulation ( G f ), fuzzy information entropy ( H f ), fuzzy rough entropy ( E r f ) and fuzzy information amount ( E f ).Moreover, numerical experiments and statistical tests to evaluate the performance of the proposed new measurements are carried out.The results of the paired t -test show that the performance of the four new measurements based on FI -structures is better than that of the corresponding four measurements based on I -structures.Finally, attribute reduction algorithms based on G f and H f are presented, and clustering analysis is conducted on the reduced CIS. The experimental results show that the proposed algorithms are effective and perform well on attribute reduction according to three evaluation indicators of clustering performance. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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13. Information structures in a fuzzy set-valued information system based on granular computing.
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Li, Zhaowen, Wang, Zhihong, Song, Yan, and Wen, Ching-Feng
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GRANULAR computing , *INFORMATION storage & retrieval systems , *FUZZY sets , *HOMOMORPHISMS , *ENTROPY (Information theory) - Abstract
A fuzzy set-valued information system (FSVIS) refers to an information system (IS) whose information values are fuzzy sets. This article investigates information structures (ISts) in a FSVIS based on granular computing (GrC). First, FSVISs and homomorphism between them are introduced. Next, ISts in a FSVIS are described. The dependence and information distance between ISts are discussed, and characterizations of ISts in a FSVIS are acquired. Additionally, as an application of ISts in a FSVIS, the entropy measure of uncertainty for a FSVIS is discussed, and on the basis of this uncertainty measure, the optimal selection of ISts is investigated. The obtained consequence will be conducive to establishing a framework for GrC in a FSVIS. Last, the difference between this paper and the references for ISts in this paper is compared and discussed. [ABSTRACT FROM AUTHOR]
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- 2021
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14. A novel three-way decision method in a hybrid information system with images and its application in medical diagnosis.
- Author
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Li, Zhaowen, Zhang, Pengfei, Xie, Ningxin, Zhang, Gangqiang, and Wen, Ching-Feng
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MEDICAL imaging systems , *HYBRID systems , *INFORMATION storage & retrieval systems , *LEUKOCYTE count , *DIAGNOSIS - Abstract
Three-way decisions are effective and heuristic methods in information processing, moreover, it provides a trisecting-and-acting framework for complex problem solving. In this paper, combining with the practical application scenario, we propose a novel three-way decisions approach and apply it to medical diagnosis. First, we build an information system which is called a hybrid information system with images by considering the characteristics of the examination items of nephritis, including urinary color, urinary tuberculosis, pH, red blood cell count, urinary irritation, computed tomography, white blood cell count and so on. Second, to describe two objects of the conditional attribute set in a hybrid information system with images, we propose the hybrid distance based on Euclidean distance. Then, the tolerance relation induced by this system is constructed. In addition, considering that missing values exist in a hybrid information system with images, interval-valued numbers are used to obtain the loss function. Given different types of parameters can respond the level of the tolerance relation and the risk preference of decision makers, and the decision rules are shown in tabular forms. Finally, an illustration is showed to verify the feasibility and reasonability of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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