The objective of security analysis is to find the weak link of distribution network. The criterion based on the characteristics of distribution network was proposed for distribution network security analysis. According to the criterion, the electrical devices in the contingency set can be classified into two kinds. The first kind meets the requirement of the criterion. The rank preference optimal ordering (RPOO) was proposed to evaluate the damage degree of power system. The second kind does not meet the requirement of the criterion, and it is the weak link of distribution network. A numerical experiment shows that the method is efficient and feasible, and the proposed method can provide assistant decision-making for safety precautions.
{"title":"Research on Distribution Network Security Analysis Based on $K(N-1+k)$ Criterion and Rank Preference Optimal Ordering","authors":"Wang Zeng-ping, Yao Yuhai, Yu Junya, Yu Chentai","doi":"10.1155/2014/790736","DOIUrl":"https://doi.org/10.1155/2014/790736","url":null,"abstract":"The objective of security analysis is to find the weak link of distribution network. The criterion based on the characteristics of distribution network was proposed for distribution network security analysis. According to the criterion, the electrical devices in the contingency set can be classified into two kinds. The first kind meets the requirement of the criterion. The rank preference optimal ordering (RPOO) was proposed to evaluate the damage degree of power system. The second kind does not meet the requirement of the criterion, and it is the weak link of distribution network. A numerical experiment shows that the method is efficient and feasible, and the proposed method can provide assistant decision-making for safety precautions.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-6"},"PeriodicalIF":0.0,"publicationDate":"2014-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/790736","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64672259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions.
{"title":"Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes","authors":"Gurhan Gurarslan","doi":"10.1155/2014/396738","DOIUrl":"https://doi.org/10.1155/2014/396738","url":null,"abstract":"Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2014-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/396738","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64477913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).
针对Hilbert空间中无限非扩张映射族、变分不等式问题的解集和平衡问题的解集，提出了一种寻找公共不动点集的公共元素的混合迭代格式。在适当的条件下，得到了一些强收敛定理。我们的研究结果改进并扩展了(Chang等人(2009)、Min和Chang(2012)、Plubtieng和Punpaeng(2007)、S. Takahashi和W. Takahashi(2007)、Tada和Takahashi(2007)、Gang和Changsong(2009)、Ying(2013)、Y. Yao和J. C. Yao(2007)以及Yong-Cho和Kang(2012))的相应结果。
{"title":"Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space","authors":"Zhou Yin-ying, Cao Jiantao, Wang Ya-li","doi":"10.1155/2014/232541","DOIUrl":"https://doi.org/10.1155/2014/232541","url":null,"abstract":"We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2014-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/232541","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64394745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A quantum random walk optimization model and algorithm in network cluster server traffic control and task scheduling is proposed. In order to solve the problem of server load balancing, we research and discuss the distribution theory of energy field in quantum mechanics and apply it to data clustering. We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk. For the data clustering problem of high dimensional space, we can decompose one -dimensional quantum random walk into one-dimensional quantum random walk. In the end of the paper, we compare the quantum random walk optimization method with GA (genetic algorithm), ACO (ant colony optimization), and SAA (simulated annealing algorithm). In the same time, we prove its validity and rationality by the experiment of analog and simulation.
{"title":"A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling","authors":"Dong Yumin, Xia Shufen","doi":"10.1155/2014/818479","DOIUrl":"https://doi.org/10.1155/2014/818479","url":null,"abstract":"A quantum random walk optimization model and algorithm in network cluster server traffic control and task scheduling is proposed. In order to solve the problem of server load balancing, we research and discuss the distribution theory of energy field in quantum mechanics and apply it to data clustering. We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk. For the data clustering problem of high dimensional space, we can decompose one -dimensional quantum random walk into one-dimensional quantum random walk. In the end of the paper, we compare the quantum random walk optimization method with GA (genetic algorithm), ACO (ant colony optimization), and SAA (simulated annealing algorithm). In the same time, we prove its validity and rationality by the experiment of analog and simulation.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2014-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/818479","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64688937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a plant disease model with continuous cultural control strategy and time delay is formulated. Then, how the time delay affects the overall disease progression and, mathematically, how the delay affects the dynamics of the model are investigated. By analyzing the transendental characteristic equation, stability conditions related to the time delay are derived for the disease-free equilibrium. Specially, when , the Jacobi matrix of the model at the disease-free equilibrium always has a simple zero eigenvalue for all . The center manifold reduction and the normal form theory are used to discuss the stability and the steady-state bifurcations of the model near the nonhyperbolic disease-free equilibrium. Then, the sensitivity analysis of the threshold parameter and the positive equilibrium is carried out in order to determine the relative importance of different factors responsible for disease transmission. Finally, numerical simulations are employed to support the qualitative results.
{"title":"Stability and Sensitivity Analysis of a Plant Disease Model with Continuous Cultural Control Strategy","authors":"Zhonghua Zhang, Yaohong Suo","doi":"10.1155/2014/207959","DOIUrl":"https://doi.org/10.1155/2014/207959","url":null,"abstract":"In this paper, a plant disease model with continuous cultural control strategy and time delay is formulated. Then, how the time delay affects the overall disease progression and, mathematically, how the delay affects the dynamics of the model are investigated. By analyzing the transendental characteristic equation, stability conditions related to the time delay are derived for the disease-free equilibrium. Specially, when , the Jacobi matrix of the model at the disease-free equilibrium always has a simple zero eigenvalue for all . The center manifold reduction and the normal form theory are used to discuss the stability and the steady-state bifurcations of the model near the nonhyperbolic disease-free equilibrium. Then, the sensitivity analysis of the threshold parameter and the positive equilibrium is carried out in order to determine the relative importance of different factors responsible for disease transmission. Finally, numerical simulations are employed to support the qualitative results.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2014-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/207959","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64388308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Based on a fourth order compact difference scheme, a Richardson cascadic multigrid (RCMG) method for 2D Poisson equation is proposed, in which the an initial value on the each grid level is given by the Richardson extrapolation technique (Wang and Zhang (2009)) and a cubic interpolation operator. The numerical experiments show that the new method is of higher accuracy and less computation time.
基于四阶紧凑差分格式，提出了二维泊松方程的Richardson级联多网格(RCMG)方法，该方法利用Richardson外推技术(Wang and Zhang(2009))和三次插值算子给出每个网格层上的初始值。数值实验表明，该方法具有较高的精度和较短的计算时间。
{"title":"Richardson Cascadic Multigrid Method for 2D Poisson Equation Based on a Fourth Order Compact Scheme","authors":"Li Ming, Li Chen-liang","doi":"10.1155/2014/490540","DOIUrl":"https://doi.org/10.1155/2014/490540","url":null,"abstract":"Based on a fourth order compact difference scheme, a Richardson cascadic multigrid (RCMG) method for 2D Poisson equation is proposed, in which the an initial value on the each grid level is given by the Richardson extrapolation technique (Wang and Zhang (2009)) and a cubic interpolation operator. The numerical experiments show that the new method is of higher accuracy and less computation time.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-6"},"PeriodicalIF":0.0,"publicationDate":"2014-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/490540","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64518911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula for it.
{"title":"A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums","authors":"Liu Miaohua, L. Xiaoxue","doi":"10.1155/2014/845845","DOIUrl":"https://doi.org/10.1155/2014/845845","url":null,"abstract":"The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula for it.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-5"},"PeriodicalIF":0.0,"publicationDate":"2014-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/845845","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64706539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xu Hong-lin, Yang Han-bing, Gao Cui-fang, Zhu Ping
Based on the community structure characteristics, theory, and methods of frequent subgraph mining, network motifs findings are firstly introduced into social network analysis; the tendentiousness evaluation function and the importance evaluation function are proposed for effectiveness assessment. Compared with the traditional way based on nodes centrality degree, the new approach can be used to analyze the properties of social network more fully and judge the roles of the nodes effectively. In application analysis, our approach is shown to be effective.
{"title":"Social Network Analysis Based on Network Motifs","authors":"Xu Hong-lin, Yang Han-bing, Gao Cui-fang, Zhu Ping","doi":"10.1155/2014/874708","DOIUrl":"https://doi.org/10.1155/2014/874708","url":null,"abstract":"Based on the community structure characteristics, theory, and methods of frequent subgraph mining, network motifs findings are firstly introduced into social network analysis; the tendentiousness evaluation function and the importance evaluation function are proposed for effectiveness assessment. Compared with the traditional way based on nodes centrality degree, the new approach can be used to analyze the properties of social network more fully and judge the roles of the nodes effectively. In application analysis, our approach is shown to be effective.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"08 1","pages":"1-6"},"PeriodicalIF":0.0,"publicationDate":"2014-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/874708","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64721045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codesn+l,M,d,(m,1)qbased on subspaces of type(m,1)in singular linear spaceFq(n+l)over finite fieldsFqare presented. Then, we prove that codes based on subspaces of type(m,1)in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures inFq(n+l).
{"title":"Bounds on Subspace Codes Based on Subspaces of Type(m,1)in Singular Linear Space","authors":"You Gao, G. Wang","doi":"10.1155/2014/497958","DOIUrl":"https://doi.org/10.1155/2014/497958","url":null,"abstract":"<jats:p>The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codes<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>based on subspaces of type<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math>in singular linear space<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant=\"double-struck\">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>over finite fields<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>are presented. Then, we prove that codes based on subspaces of type<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\"><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math>in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant=\"double-struck\">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>.</jats:p>","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2014 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/497958","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64520366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define the rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.
{"title":"Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data","authors":"Chen Li, Gong Zeng-tai, Duan Gang","doi":"10.1155/2013/542153","DOIUrl":"https://doi.org/10.1155/2013/542153","url":null,"abstract":"Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define the <path id=\"x1D70E\" d=\"M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109\u0000q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z\" /> <path id=\"x1D706\" d=\"M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5\u0000q27 -249 51 -392q7 -46 23 -46q24 0 70 60z\" /> rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2013 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2013-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/542153","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64147388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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