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A New Method of Aggregation of fuzzy number Based on the Dempster/Shafer Theory

The Second International Conference on Game Theory and Applications (CMGTA’2007)

作者： Xing Cai~+ Xin-bo Zhang College of Information and Electronic Engineering Zhejiang Gongshang University HangZhou China 310035

＜正＞Experts use natural language in the unstructured decision problem,when they are establishing value by pairwise comparison.It can fully express experts’ will,and make experts’ scoring more scientific. fuzzy numbers are introduced,then propose a expansionary 9-point scale and new fuzzy unstructured decision-making.At last,this paper explains rationality of this way by one case.

关键词： unstructured decision making natural language expansionary 9-point scale fuzzy number related weights synthetic weights.

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A New Method of Aggregation of Fuzzy Number Based on the Dem...

Hybrid multiple attribute decision making model based on entropy

2011 Chinese Control and Decision Conference（CCDC）

作者： Bing Yi Kang,Ya Juan Zhang,Xin Yang Deng and Yong Deng are with School of Computer and Information Sciences,Southwest University,Chongqing,400715,China Ji Yi Wu is with Hangzhou Key Lab of E-Business and Information Security,Hangzhou Normal University,Hangzhou,Zhejiang,310036,China Xiao Hong Sun is also with College of Food Science and Technology,Shanghai Ocean University,Shanghai,201306,China Yong Deng is also with Key Subject Laboratory of National defense for Radioactive Waste and Environmental Security,Southwest University of Science and Technology,Mianyang,Sichuan,621010,China,Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education,Xiangtan University,Xiangtan,Hunan,411105,China and School of Electronics & Information Technology,Shanghai Jiao Tong University,Shanghai,200240,China

There exists lots of fuzzy and imprecise information with the development of society and technology.How to combine and evaluate these information becomes significant.This paper takes the proportion of the membership function values into consideration and makes use of each interval area value compared with the whole area of fuzzy number to measure the distribution of the membership function values.A triangular membership function was used to represent the fuzzy numbers.Then,the BPA of each point selected can be gained through multiplying the membership function values with their proportion respectively.At last,the D/S Theory was used to aggregate the fuzzy numbers.Through an instance,we get an acceptable result.

关键词： D/S theory fuzzy number BPA

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Journal of Systems Engineering and Electronics 2007年第1期18卷 72-75页

作者： Wang Wei Cui Mingming Dept. of Management Science Naval Univ. of Engineering Wuhan 430033 P.R. China

From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept： project entropy and the de... 详细信息

关键词： Decision making Project entropy Hybrid multiple attribute fuzzy number

A Bayesian Network Approach for Offshore Risk Analysis Through Linguistic Variables

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China Ocean Engineering 2007年第3期21卷 371-388页

作者： Ren J. Wang J. Jenkinson I. Xu D. L. Yang J. B. School of Engineering Liverpool John Moores University Liverpool L 3 3 AF UK Manchester Business School The University of Manchester Manchester M 60 1 QD UK

This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks （ BNs）. In this paper, linguistic probabilities are used to describe occurrence likelihood of hazardous events that may cause possible accidents in offshore operations. In order to use fuzzy information, an f-weighted valuation function is proposed to transform linguistic judgements into crisp probability distributions which can be easily put into a BN to model causal relationships among risk factors. The use of linguistic variables makes it easier for human experts to express their knowledge, and the transformation of linguistic judgements into crisp probabilities can significantly save the cost of computation, modifying and maintaining a BN model. The flexibility of the method allows for multiple forms of information to be used to quantify model relationships, including formally assessed expert opinion when quantitative data are lacking, or when only qualitative or vague statements can be made. The model is a modular representation of uncertain knowledge caused due to randomness, vagueness and ignorance. This makes the risk analysis of offshore engineering systems more functional and easier in many assessment contexts. Specifically, the proposed f-weighted valuation function takes into account not only the dominating values, but also the a-level values that are ignored by conventional valuation methods. A case study of the collision risk between a Floating Production, Storage and Off-loading （FPSO） unit and the anthorised vessels due to human elements during operation is used to illustrate the application of the proposed model.

关键词： Risk analysis fiweighted valuation function Bayesian networks fuzzy number linguistic probability off-shore engineering systems

A METHOD OF SOLVING THE fuzzy FINITE ELEMENT EQUATIONS IN MONOSOURCE fuzzy numberS

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Applied Mathematics and Mechanics(English Edition) 2000年第11期21卷 1272-1276页

作者：刘长虹陈虬 Department of Applied Mechanics and Engineering Southwest Jiaotong University Chengdu P R China

For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modem engineering design.

关键词： fuzzy number fuzzy stochastic finite element method (FSFEM) Edgeworth series

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

Two-echelon production-inventory system with fuzzy production rate and promotional effort dependent demand

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Journal of Management Analytics 2015年第1期2卷 72-92页

作者： S.Priyan M.Palanivel R.Uthayakumar Department of Mathematics The Gandhigram Rural Institute-Deemed UniversityGandhigram624302DindigulTamil NaduIndia

Intelligent manufacturing design of a complex production-inventory system becomes a key issue for the organization of responsiveness to uncertainties.This paper addresses a two-echelon production-inventory model for a non-repairable product where the system consists of single manufacturer and single retailer.The manufacturer procures raw material(which also contains imperfect raw materials)from an outside supplier then proceeds to convert perfect-quality raw material as a finished product,and finally delivers to the retailer.In this study we assume that the demand is sensitive to promotional efforts/sales teams’initiatives and the production rate is uncertain but possible to describe with a triangular fuzzy number.Then we use the signed distance method to defuzzify the fuzzy joint total cost and an analytical method is employed to achieve the optimal solutions so that the total costs of both manufacturer and retailer are minimized.An efficient algorithm is developed to design an intelligent manufacturing strategy such as optimal production lot-size,backlogging and the initiatives of sales teams.A numerical example and sensitivity analysis are given to demonstrate the application of the proposed model.

关键词： fuzzy number signed distance method production rate

An Equivalent Condition for （K） Integrability of fuzzy-valued Mappings

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Northeastern Mathematical Journal 2007年第1期23卷 63-70页

作者：李宝麟张迪 Department of Mathematics Norhwest Normal University Lanzhou 730070

In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equival... 详细信息

关键词： fuzzy number fuzzy set-valued mapping McShang integral Pettis integral （K） integral

Distinguished Representation of Criteria Based on Trapezoidal fuzzy numbers and fuzzy Memberships in Selection of Contractors

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Journal of Donghua University(English Edition) 2016年第5期33卷 713-718页

作者：代涛刘幸高睿陆伟 School of Civil Engineering Wuhan University Wuhan Municipal Engineering Design and Research Institute Co. Ltd.

More attention has been drawn to the selection of contractors in recent years,but little research has been conducted on distinguishing representation of performance values for qualitative and quantitative criteria in one decision-making(DM) problem yet.Thus a novel method based on fuzzy number is proposed to solve the representation issue,in which linguistic terms and fuzzy memberships are used to separately describe qualitative and quantitative criteria,and then the linguistic terms are translated into fuzzy numbers which will be defuzzified and unified with fuzzy memberships.The novel method is used to develop a synthetic decision model for selection of contractors.The model is developed to verify the feasibility of the novel method,which(1) builds a twolevel criteria system based on survey and literature summary;(2)utilizes the analytic network process(ANP) to determine criteria weights;(3) uses the novel method to make different representations of performance values for qualitative and quantitative criteria in one DM problem and then unifies different representations for decision matrices;(4) utilizes three multi-criteria decision-making(MCDM) methods containing simple additive weighting(SAW),technique for order preference by similarity to ideal solution(TOPSIS) and complex proportional assessment(COPRAS) to deal with decision matrices.Besides,a case of contractor selection is given to check the novel method by applying developed model,and the case results show that the novel method can suitably solve the representation issue of the performance values for two types of criteria as well as simplify the processes of TOPSIS and COPRAS.

关键词： selection of contractors representation of performance values fuzzy number multi-criteria decision-making(MCDM)