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Comparison of fuzzy numbers using possibility programming: Comments and new concepts

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2002年第6-7期43卷 833-840页

作者： Iskander, MG American Univ Dept Econ Cairo Egypt

Comparing fuzzy numbers, using the possibility programming approach, was presented by Negi and Lee [1]. In this paper, we are going to state some comments concerning their approach. The case of comparing different fuzzy numbers is considered. Also, the formulation of the crisp problem in the case of fuzzy linear programming and fuzzy multiobjective linear programming is discussed, and a new modified model, in each case, is stated. Our proposed approach is illustrated by numerical examples. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： possibility programming fuzzy linear programming fuzzy multiobjective programming

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A possibility programming approach for stochastic fuzzy multiob jective linear fractional programs

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2004年第10-11期48卷 1603-1609页

作者： Iskander, MG Amer Univ Cairo Dept Econ Cairo Egypt

In this paper, a suggested program with fuzzy linear fractional objectives and stochastic fuzzy constraints is considered. The fuzzy coefficients and scalars in the linear fractional objectives, and the left-hand side fuzzy coefficients of the constraints can be either trapezoidal or triangular fuzzy,numbers. The right-hand sides of the constraints are considered independent random variables with known distribution functions. A modified possibility programming approach, within the chance-constrained, is utilized to transform the suggested program to its equivalent deterministic-crisp multiobjective linear program, whether in the case of exceedance possibility or the case of strict exceedance possibility. A numerical example illustrates the proposed method. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： possibility programming chance-constrained stochastic fuzzy multiobjective linear fractional programs

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A computational comparison between two evaluation criteria in fuzzy multiobjective linear programs using possibility programming

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2008年第11期55卷 2506-2511页

作者： Iskander, Maged George Amer Univ Cairo Dept Math Cairo Egypt

In this paper, a fuzzy multiobjective linear programming model is presented. Both the objective functions and the constraints are considered fuzzy. The coefficients of the decision variables in the objective functions and in the constraints, as well as the right-hand side of the constraints are assumed to be fuzzy numbers with either trapezoidal or triangular membership functions. The possibility programming approach is utilized to transform the fuzzy model to its crisp equivalent. A comparison between the global criterion method and the distance functions method, as two evaluation criteria, is illustrated by a computational study. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： fuzzy multiobjective linear programming possibility programming global criterion method distance functions method

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A ROBUST MULTI-CRITERIA FUZZY programming PROBLEM CONSIDERING possibility MEASURE

A ROBUST MULTI-CRITERIA FUZZY PROGRAMMING PROBLEM CONSIDERIN...

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1st International Symposium on Intelligent Informatics (ISII 2008)

作者： Hasuike, Takashi Ishii, Hiroaki Osaka Univ Grad Sch Informat Sci & Technol Suita Osaka 5650871 Japan

This paper considers a multi-criteria mathematical decision model including fuzzy variables. As the proposed model is not well-defined due to fuzzy variables, thus to solve them directly and analytically, the possibility measure is introduced. Then, in order to aggregate the multi-criteria objective functions into the single-criterion, the fuzzy compromise programming model is proposed. Furthermore, by introducing the interval of each weight to the objective functions, the proposed model is reformulated as a robust programming problem. Since this problem is a semi-infinite programming problem, the an efficient algorithm. is developed using the linearity of the proposed model. Finally, a numerical example is provided to compare proposed models with the basic model.

关键词： Multi-criteria programming possibility programming Robust programming Semi-infinite programming

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A fuzzy weighted additive approach for stochastic fuzzy goal programming

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APPLIED MATHEMATICS AND COMPUTATION 2004年第2期154卷 543-553页

作者： Iskander, MG Amer Univ Cairo Dept Econ Cairo Egypt

In this paper, a certain structure for the stochastic fuzzy goal programming problem is presented. The goal constraints are considered stochastic and fuzzy, with fuzziness in inequalities, while the aspiration levels are assumed independent random variables with known distribution functions. The chance-con strained approach is utilized to transform the stochastic constraints to their deterministic equivalent. On the other hand, when any preemptive priority structure can not be determined, a fuzzy weighted additive approach is proposed, through the possibility programming technique that relies on the a-cut approach, to formulate a deterministic-crisp model. The suggested approach is illustrated by a numerical example. (C) 2003 Elsevier Inc. All rights reserved.

关键词： stochastic fuzzy goal programming chance-constrained approach fuzzy weighted additive model possibility programming

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Evaluating decision-making units under uncertainty using fuzzy multi-objective nonlinear programming

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INFOR 2017年第1期55卷 1-15页

作者： Angiz, Madjid Langroudi Zerafat Nawawi, Mohd Kamal Mohd Khalid, Ruzelan Mustafa, Adli Emrouznejad, Ali John, Robert Kendall, Graham Univ Utara Malaysia Sch Quantitat Sci Sintok Malaysia Univ Sains Malaysia Sch Math Sci Gelugor Malaysia Aston Univ Aston Business Sch Birmingham W Midlands England Univ Nottingham Sch Comp Sci ASAP Res Grp Nottingham England Univ Nottingham Malaysia Campus Sch Comp Sci Semenyih Malaysia

This paper proposes a new method to evaluate decision-making units (DMUs) under uncertainty using fuzzy data envelopment analysis (DEA). In the proposed multi-objective nonlinear programming methodology, both the objective functions and the constraints are considered fuzzy. This model is comprehensive in dealing with uncertainty, in the sense that coefficients of the decision variables in the objective functions and in the constraints, as well as the DMUs under assessment, are assumed to be fuzzy numbers with triangular membership functions. A comparison between the current fuzzy DEA models and the proposed method is illustrated by a numerical example.

关键词： Fuzzy DEA membership function fuzzy multi-objective linear programming possibility programming

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Possibilistic programming in production planning of assemble-to-order environments

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FUZZY SETS AND SYSTEMS 2001年第1期119卷 59-70页

作者： Hsu, HM Wang, WP Natl Chiao Tung Univ Dept Ind Engn & Management Hsinchu 30050 Taiwan

For the sake of alleviating the influences of demand uncertainty in assemble-to-order (ATO) environments, the strategies of regulating dealers' forecast demands, determining appropriate safety stocks, and deciding the numbers of key machines are usually adopted by manufacturers. In this paper, we propose a possibility linear programming model to manage these production planning problems. The proposed model accomplishes forecasting adjustments, material management, and production activities. Because of price fluctuations, material obsolescence, and the time value of, capital. the ambiguity of cost is considered in the objective function of the model. We substituted the fuzzy objective function with three crisp objectives: minimizing the most possible cost, maximizing the possibility of obtaining lower cost, and minimizing the risk of obtaining higher cost. Zimmermann's fuzzy programming method is then applied for achieving an overall satisfactory compromise solution. Finally, an example is given to illustrate our model. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： assemble-to-order forecast demands safety stock possibility programming

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Robust and minimum spanning tree in fuzzy environment

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INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2019年第5期10卷 513-524页

作者： Dey, Arindam Mondal, Sahanur Pal, Tandra Saroj Mohan Inst Technol Dept Comp Sci & Engn Hooghly India Natl Inst Technol Dept Comp Sci & Engn Durgapur India

This paper proposes an algorithm to find the fuzzy minimum spanning tree (FMST) of an undirected weighted fuzzy graph, in which mixed fuzzy numbers, either triangular or trapezoidal, are used to represent the lengths/costs of the arcs. In the proposed algorithm, we incorporate the uncertainty in Kruskal's algorithm for MST using fuzzy number as arc length. The concept of possibility programming is used to compare between the fuzzy number (i.e., costs of arcs) and addition operation of fuzzy numbers is used to find the cost of the spanning tree. We also investigate the robust version of the FMST problem. We define two measures for robustness of an FMST: absolute robustness and relative robustness. We characterize the fuzzy worst case scenarios for a given fuzzy spanning tree for both the measures. The corresponding fuzzy robust spanning trees are respectively defined as absolute robust fuzzy spanning tree (ARFST) and relative robust fuzzy spanning tree (RRFST). We extend Kruskal's algorithm to compute the ARFST and RRFST in fuzzy environment. An example of fuzzy graph is used to illustrate the effectiveness of the proposed methods.

关键词： possibility programming robust spanning tree Kruskal's algorithm minimum spanning tree triangular fuzzy number trapezoidal fuzzy number fuzzy graph fuzzy minimum spanning tree absolute fuzzy robust spanning tree relative fuzzy robust spanning tree

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Particle Swarm Optimization for Vehicle Routing Problem with Uncertain Demand

Particle Swarm Optimization for Vehicle Routing Problem with...

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4th IEEE International Conference on Software Engineering and Service Science (ICSESS)

作者： Chen, Jun-Qi Li, Wan-Ling Murata, Tomohiro Waseda Univ Grad Sch Informat Prod & Syst Kitakyushu Fukuoka 8080135 Japan

ISBN: (纸本)9781467350006

In this paper, we deal with the vehicle routing problem where vehicles have finite capacities and demands of customers are uncertain. We represent the uncertain demands by fuzziness and interpret them as possibility distributions. According to the same consideration as the fuzzy programming with recourse, we treat the influence of the fuzzy of customers' demands as recourse cost. Defining the fuzzy number as it's the generalized mean value, the proposed model is equivalent to an ordinary programming problem and then a solution method based on Particle Swarm Optimization (PSO) can be proposed to give the best solution of the problem. Finally, some examples are given to illustrate the two-stage model and the solution algorithm.

关键词： Vehicle Routing Problem possibility programming Particle Swarm Optimization

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Particle Swarm Optimization for Vehicle Routing Problem with Uncertain Demand

Particle Swarm Optimization for Vehicle Routing Problem with...

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2013 IEEE 4th International Conference on Software Engineering and Service Science

作者： Jun-Qi Chen Wan-Ling Li Tomohiro Murata Graduate School of Information Production and Systems University of Waseda 1-15-4202 Wakamatsu-kuKitakyushu-shi808-0135Japan Graduate School of Information Production and Systems University of Waseda 2-7 Wakamatsu-kuKitakyushu-shi808-0135Japan

ISBN: (纸本)9781467349994

In this paper,we deal with the vehicle routing problem where vehicles have finite capacities and demands of customers are *** represent the uncertain demands by fuzziness and interpret them as possibility *** to the same consideration as the fuzzy programming with recourse,we treat the influence of the fuzzy of customers’ demands as recourse *** the fuzzy number as it’s the generalized mean value,the proposed model is equivalent to an ordinary programming problem and then a solution method based on Particle Swarm Optimization（PSO） can be proposed to give the best solution of the ***,some examples are given to illustrate the two-stage model and the solution algorithm.

关键词： Vehicle Routing Problem possibility programming Particle Swarm Optimization

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