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Sufficient and Necessary Condition of credibility measure

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Sufficient and Necessary Condition of Credibility Measure

第三届不确定系统年会

作者： Xiang Li Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

＜正＞ Possibility measure is widely used in fuzzy set theory. However, possibility measure is not self-dual. credibility measure is a self-dual one. This paper proves the uniqueness theorem between possibility measur... 详细信息

关键词： Fuzzy variable Possibility measure credibility measure

Parallel Machine Scheduling Models with Fuzzy Parameters and Precedence Constraints: A credibility Approach

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Journal of Beijing Institute of Technology 2007年第2期16卷 231-236页

作者：侯福均吴祈宗 School of Management and Economics Beijing Institute of Technology

A method for modeling the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure is provided. For the given n jobs to be processed on m machines, it is assumed that the processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive, crisp numbers. Based on credibility measure, three parallel machine scheduling problems and a goal-programming model are formulated. Feasible schedules are evaluated not only by their objective values but also by the credibility degree of satisfaction with their precedence constraints. The genetic algorithm is utilized to find the best solutions in a short period of time. An illustrative numerical example is also given. Simulation results show that the proposed models are effective, which can deal with the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure.

关键词： parallel machine scheduling programming model possibility measure credibility measure fuzzy number genetic algorithm

Fuzzy-TOPSIS Method with Multi-goal

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Journal of Beijing Institute of Technology 2009年第1期18卷 112-116页

作者：逄金辉张强 Administrative Institute of Information Resources Beijing Institute of Technology School of Management and Economics Beijing Institute of Technology

To develop the technique for order preference by similarity to an ideal solution, namely, TOPSIS method with multi-goal in fuzzy decision environment. Firstly, a new approach to constructing fuzzy decision matrix by Choquet integral was proposed in multi-goal decision system. Secondly, the concepts of fuzzy positive-ideal solution and fuzzy negative-ideal solution related to the fuzzy decision matrix were given. Finally, the credibility measure was adopted to calculate the distances to fuzzy positive-ideal solution and fuzzy negative-ideal solution. The presented fuzzy-TOPSIS method embodies well both the predetermined preferences and the weights of goals.

关键词： credibility measure ideal solution Choquet integral

Fuzzy Global Stability Analysis of the Dynamics of Malaria with Fuzzy Transmission and Recovery Rates

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American Journal of Operations Research 2021年第6期11卷 257-282页

作者： Yves Tinda Mangongo Joseph-Désiré Kyemba Bukweli Justin Dupar Busili Kampempe Department of Mathematics and Computer Science Faculty of Sciences University of Kinshasa Kinshasa D.R. Congo

In this paper, fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (), we reach the model disease-free equilibrium. Using Choquet integral, the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible, Exposed, Infected, Recovered, susceptible-Susceptible, Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium is globally asymptotically stable if or if the basic reproduction number is less than one (). Whe

关键词： Malaria Fuzzy Analysis Fuzzy Basic Reproduction Number Fuzzy Variable credibility measure Fuzzy Equilibrium Fuzzy Global Stability

Fuzzy Quadratic Minimum Spanning Tree Problem

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Fuzzy Quadratic Minimum Spanning Tree Problem

第二届不确定系统年会

作者： Jinwu Gao Mei Lu Uncertainty Theory Laboratory, Department of Mathematical Sciences Tsinghua University, Beijing 100084, China

In this paper, a fuzzy quadratic minimum spanning tree problem is formulated as expected value model, chance-constrained programming and dependent-chance programming according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a simulation-based genetic algorithm using Prufer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents. Finally, a numerical example is provided for illustrating the effectiveness of the genetic algorithm.

关键词： Minimum spanning tree fuzzy programming genetic algorithm credibility measure

The Fuzzy Weighted Quadratic Minimum Spanning Tree and its Hybrid Genetic Algorithm

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The Fuzzy Weighted Quadratic Minimum Spanning Tree and its H...

第三届不确定系统年会

作者： Linzhong Liu Lixing Yang Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China

＜正＞ The quadratic minimum spanning tree problem is to find a spanning tree in a given graph such that the total cost consists of the direct cost and interactive cost is minimum and is known to be NP-hard. In this paper, the quadratic minimum spanning tree problem with fuzzy weights is firstly formulated as the chance-constrained programming by using the possibility measure and the credibility measure. Then an oriented tree and knowledge-based hybrid genetic algorithm is designed for solving the proposed fuzzy programming models. Finally, a numerical example is given to verify the efficiency of the designed algorithm.

关键词： fuzzy set credibility measure spanning tree genetic algorithm quadratic spanning tree

Linear Rank Tests with Imprecise Observations

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Linear Rank Tests with Imprecise Observations

第九届中国不确定系统年会、第五届中国智能计算大会、第十三届中国青年信息与管理学者大会

作者： G.Hesamian S.M.Taheri Department of Mathematical Sciences Isfahan University of Technology

This paper extends the problem of general non-parametric linear rank tests in the case where the available samples of observations are imprecise and the level of significance is also a fuzzy *** do this,the usual concepts of test statistic, and critical value are extended to the fuzzy test statistic and fuzzy critical value,by using the a-cuts *** paper also provides an example to clarify the approach in this paper.

关键词： fuzzy statistic hypothesis test linear rank test credibility measure

Some Ranking Methods to Data Envelopment Analysis

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Some Ranking Methods to Data Envelopment Analysis

第五届中国不确定系统年会

作者： Meilin Wen Department of Mathematical Sciences Tsinghua University,Beijing 100084,China

＜正＞Most efficiency measures in DEA estimate the distance between DMUs to an efficient frontier as their relative *** there comes forth another method which uses the distance to the inef- ficient frontier to estimate the *** paper wants to rank all the DMUs by the Hurwicz criterion, which attempts to find a middle ground between the distances to the efficient frontier and to the inefficient *** varying the parameter in the Hurwicz cri- terion,the ranking method can present various forms. This method can rank all the DMUs including effi- cient ones and inefficient *** many cases,the inputs and outputs can not be given exactly,which can be considered to be *** order to rank the DMUs with fuzzy data,we give the ranking method in DEA under fuzzy environment based on credibility ***,we provide some numerical exam- ples to illustrate the ranking methods that this paper introduced.

关键词： Data Envelopment Analysis Ranking Method credibility measure Hurwicz Criterion Fuzzy Programming

Fuzzy Maximum Likelihood Estimator

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Fuzzy Maximum Likelihood Estimator

第三届中国智能计算大会

作者： Jicai Liu,Huanbin Liu College of Mathematics and Information Sciences,Shanghai Normal University,Shanghai 200234 College of Mathematics and Information sciences,Huanggang Normal University,Hubei 438000

＜正＞This paper proposes the new concept of fuzzy maximum likelihood estimator based on credibility distribution of fuzzy *** invariance properties of fuzzy maximum likelihood estimator are *** convergence under give... 详细信息

关键词： credibility measure fuzzy variable maximum principle maximum likelihood estimator