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Inexact two-phase fuzzy programming and its application to municipal solid waste management

ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2012年第8期25卷 1529-1536页

作者： Lu, H. W. Huang, G. H. Xu, Y. He, L. N China Elect Power Univ Sino Canada Resources & Environm Res Acad Beijing 102206 Peoples R China Chinese Acad Environm Planning Beijing 100012 Peoples R China

In this study, an inexact two-phase fuzzy programming approach was proposed for municipal solid waste management. Through introducing multiple control variables, objective function and constraints of the management model were relaxed under different levels, and compromised decision schemes with a high satisfactory level can be expected. Compared to the previous studies, it showed sound capability in identifying key factors and/or input conditions that may significantly affect system outputs, and thus facilitating the decision maker adjusting current system status to benefit the future management. A MSW management problem was provided to demonstrate the performance of the approach. Special parameters having significant or no impact on system performance were specified, which were then respectively changed to constitute two scenarios. The scenario analysis proved the accuracy of the model in identifying key factors. It was also found that the average satisfactory level of optimal solutions from the two-phase model was [0.287, 0.829], which was higher than that obtained from the conventional approach (i.e. [0.130, 0.804]), indicating the advantage of the proposed approach in searching for optimal solutions with high satisfactory level. (C) 2012 Published by Elsevier Ltd.

关键词： fuzzy programming Mixed integer Uncertainty Municipal solid waste Two-phase Interval

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A note on solving multicriteria transportation-location problems by fuzzy programming

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2001年第2期18卷 149-164页

作者： Ehrgott, M Verma, R Univ Auckland Dept Engn Sci Auckland New Zealand Univ Kaiserslautern Dept Math D-67653 Kaiserslautern Germany

Transportation-location problems are generalizations of the classical transportation problem in which, in addition to seeking the quantities to be transported from supply points to demand points by various vehicles, it is also necessary to find, at the same time, the "optimal" locations of one or several supply points in Euclidean space with respect to a fixed and known set of demand points, where these new supply points and vehicles are supposed to have certain limitations on their capacity to supply the product. Since the various decision makers involved in the process will have different opinions of the importance of the existing facilities, a multicriteria problem with several objectives arises. In this paper, we use fuzzy techniques to find an optimal compromise solution. We prove that the final compromise solution is weakly Pareto optimal and Pareto optimal, if it is unique.

关键词： transportation-location problem multicriteria optimization Pareto optimal solution fuzzy programming linear membership function

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An aspect of bilevel interval linear fractional transportation problem with disparate flows: a fuzzy programming approach

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2023年第6期14卷 2276-2288页

作者： Arora, Ritu Jaggi, Chandra K. K. Univ Delhi Dept Math Keshav Mahavidyalaya Delhi India Univ Delhi Dept Operat Res Delhi India

In present times, the e-commerce industry has become a crucial platform between the manufacturers and the common man. There might arise some situations in the market due to which manufacturers are not able to estimate the exact demand for their products, which may result in excess production. Moreover, the demand for the products in the market depends on the purchasing power of the common man. The decrease in purchasing power results in the low sale of the products. This uncertain situation of the market has been depicted by Bilevel Interval Linear Fractional Transportation Problem with distinct flows. The supply, demand, and cost coefficients in the objective functions at two levels are interval parameters. The two-level problem comprises of delivery of products from manufacturers to e-warehouses at the upper level and then to customers at the lower level. At upper level, flow is enhanced since the goods which are manufactured by the industries in large quantities need to be sold out. At lower level, flow is restricted while transporting the goods from e-warehouses to customers. Further, in order to promote the sale of the products, e-websites offer the customers free delivery of the products at their doorsteps. At the same time, they also pick the goods from them if the products are damaged or not of their choice or for any other reason. This in turn incurs the additional cost to the e-websites. The constraints in this defined problem are mixed. The interval parameters in the defined problem are tackled using the concept of centre and width of the interval. This converts the bilevel problem into a bilevel multi-objective transportation problem. A satisfactory solution to the problem is obtained by the fuzzy programming and goal programming approaches. A numerical is illustrated explaining the methodology. Further, the solutions are compared through these two techniques.

关键词： Interval uncertainty Enhanced flow Restricted flow Linear fractional transportation problem Bilevel programming fuzzy programming Goal programming

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AN ELEMENTARY fuzzy-programming LANGUAGE

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fuzzy SETS AND SYSTEMS 1993年第1期57卷 55-73页

作者： MORALESBUENO, R CONEJO, R DELACRUZ, JLP CLARES, B UNIV MALAGA FAC INFORMATDPTO LENGUAJES & CIENCIAS COMPUTACE-29071 MALAGASPAIN UNIV GRANADA FAC CIENCIASDPTO LENGUAJES & SISTEMAS INFORMATE-18071 GRANADASPAIN

In this paper, we define a fuzzy imperative programming language (called L), powerful enough to express crisp and fuzzy algorithms. Its small instruction set is designed to enhance readability, and it is proved before that the class of functions that can be programmed in L is equivalent to the class of functions computed by a W-Turing machine and to the W-recursive functions. The language is defined by means of an attribute grammar, and we present some examples of programs and their execution. A compiler has been built for the language, whose features are briefly described.

关键词： fuzzy programming fuzzy COMPUTABILITY fuzzy LANGUAGE

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Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2000年第6期83卷 1-9页

作者： Sakawa, M Nishizaki, I Uemura, Y Kubota, K Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 7398527 Japan Juken Sangyou Co Ltd Prod Projects Dev Dept Hatsukaichi 7380022 Japan

This paper considers the multilevel linear programming problem with fuzzy parameters, and proposes an interactive fuzzy programming method. Lai and colleagues recently proposed a fuzzy programming method for the multilevel linear programming problem, but there remained the possibility that the procedure could arrive at an undesirable solution. This paper is an attempt to cope with this problem. Extending the multilevel linear programming problem to the problem with fuzzy parameters, an interactive fuzzy programming method is proposed as follows. The fuzzy goal is defined for the objective function of the decision-maker of each level. The decision-maker except for the lowest level subjectively defines the minimum tolerance for satisfaction. Then, by considering the satisfaction ratio among the levels and interactively updating the minimum tolerance of the decision-maker, if necessary, the satisficing solution is efficiently derived, while considering the intention of the decision-makers at the upper level as well as the balance of the achieved satisfactions among the levels. Lastly, a numerical example is investigated for the three-level linear programming problem with fuzzy parameters, and the validity and effectiveness of the proposed method are demonstrated. (C) 2000 Scripta Technica.

关键词： multilevel linear programming problem with fuzzy parameter fuzzy programming fuzzy goal interactive method

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Integrating Decision Analysis with fuzzy programming: Application in Urban Water Distribution System Operation

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2014年第5期140卷 638-648页

作者： Xu, T. Y. Qin, X. S. Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore Nanyang Technol Univ Earth Observ Singapore Singapore 639798 Singapore

Water-distribution operation is an essential part of an urban water-supply system to deliver high-quality water to consumers. Management of such an operation may involve deliberations of operation cost, system capacity, and environmental restriction, and is convoluted with many forms of uncertainties. In this paper, an integrated fuzzy programming and decision analysis (IFPDA) approach was proposed for a multilayer urban water-distribution system management under uncertainty. The system consisted of two water sources, four treatment plants, seven reservoirs, and seven consuming zones. Uncertain information associated with water demands, water-treatment capacities, water-transfer cost, and leakage rate was described by a trapezoidal-shaped fuzzy set and embedded into a fuzzy programming framework. The balance between the satisfaction degree of achieving the system objective and feasibility level of meeting the related constraints was analyzed by fuzzy inference procedures. The results indicate that the IFPDA approach was advantageous in (1)dealing with fuzzy uncertainties in the objective function, both sides of the model constraints, and the context of an urban water-distribution system management;(2)helping analyze tradeoffs between minimization of operation cost and reliability of running the system;and (3)linking optimization model outputs with decision analysis.

关键词： Uncertainty Trapezoidal-shaped fuzzy sets Decision-making Urban water-distribution system fuzzy programming

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Binary behavior of fuzzy programming with piecewise linear membership functions

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IEEE TRANSACTIONS ON fuzzy SYSTEMS 2007年第3期15卷 342-349页

作者： Chang, Ching-Ter Natl Changhua Univ Educ Informat & Management Changhua 500 Taiwan

The nature of vagueness, imprecision and uncertainly is fuzzy rather than crisp and/or random, especially for a multiple objectives decision-making problem. A key component of fuzzy programming is the membership function that represents a mathematical expression of level function for the decision-maker's preference. In fact, a decision-making problem involves the achievement of fuzzy goals, some of which are met while others are not because these fuzzy goals are subject to real-world constraints. To represent this situation, the binary piecewise linear membership function is then employed. In order to solve the problem, we propose a new idea of how to formulate the binary piecewise linear membership function. The formulated problem can be easily solved using common integer programming packages. In addition, an illustrative example is included for demonstrating the usefulness of the proposed model. Finally, the analytical superiority of the proposed method in terms of the execution time can be seen, through a computation experiment conduced on a set of generated test examples.

关键词： fuzzy programming nonlinear membership function

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The relationship between goal programming and fuzzy programming

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fuzzy SETS AND SYSTEMS 1997年第2期89卷 215-222页

作者： Mohamed, RH CAIRO UNIV FAC ECON & POLIT SCICAIROEGYPT

Goal programming (GP) and fuzzy programming (FP) are two approaches for solving the vector optimization problem by reducing it to a single (or sequential) objective one. These two approaches have some similarities and both of them have more than one form to handle the multiobjective problem. This paper highlights the similarities between GP and FP and answers the question how each one can lead to the other. However, we will consider in this paper the min-operator to transform the linear FP to a crisp program since this approach is more popular and applied than the others. In addition, some new forms of fuzzy programs are presented in this paper. These new forms use the concept of deviational variables of GP (and not the min-operator) to transform the FP to a crisp one. Finally, a numerical example to illustrate the relationship between the two approaches is given. (C) 1997 Elsevier Science B.V.

关键词： goal programming fuzzy programming

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fuzzy arithmetic on LR fuzzy numbers with applications to fuzzy programming

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JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2016年第1期30卷 71-87页

作者： Zhou, Jian Yang, Fan Wang, Ke Shanghai Univ Sch Management Shanghai 200444 Peoples R China

In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and exactly calculating the inverse credibility distribution of some specific arithmetical operations based on the credibility measure. As an application of the operational law, an equivalent form of the expected value operator as well as a theorem for computing the expected value of strictly monotone functions is suggested. Finally, we utilize the operational law to construct a solution framework of fuzzy programming with parameters of regular LR fuzzy numbers, and such type of fuzzy programming problems can be handled by the operational law as the classic deterministic programming without any particular solving techniques.

关键词： LR fuzzy number regular LR fuzzy number fuzzy arithmetic operational law expected value fuzzy programming

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Comparisons of interactive fuzzy programming approaches for closed-loop supply chain network design under uncertainty

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 125卷 500-513页

作者： Wu, Gen-Han Chang, Chen-Kang Hsu, Lo-Mei Yuan Ze Univ Dept Ind Engn & Management Taoyuan Taiwan Natl Dong Hwa Univ Grad Inst Logist Management Hualien Taiwan

A closed-loop supply chain network design is a facility location problem combined with forward and reverse logistics. To reflect the environmental fluctuations and the market competitiveness, recycled products will be remanufactured and sold to obtain the advantages of achieving green environmental protection and of reducing cost. This study considers the uncertain factors such as the quantity of customer product demand, the quantity of recycled used products, and the facility opening cost to design a fuzzy mixed-integer linear programming model for a closed-loop supply chain network design under uncertainty. A two-stage interactive possibilistic programming procedure is constructed to obtain a preferred compromise solution. Four fuzzy optimization approaches are embedded into the two-stage interactive possibilistic programming model and are compared. After computing experimental testing, we find that this study, based on the TH fuzzy approach, obtains a more efficient balanced compromise solution than other fuzzy approaches.

关键词： Closed-loop supply chain network Uncertainty Facility location fuzzy programming Possibilistic programming

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