基于优先模糊目标规划方法的多目标交通模型研究

交通运输系统工程与信息 ›› 2008, Vol. 8 ›› Issue (3): 40-48 .

基于优先模糊目标规划方法的多目标交通模型研究

PRAMANIK Surapati ¹, ROY Tapan Kumar ²

1 Department of Mathematics, Nandalal Ghosh B.T. College,，印度西孟加拉 743126
2 Bengal Engineering and Science University，印度西孟加拉711103

收稿日期:2008-03-06 修回日期:2008-04-19 出版日期:2008-06-25 发布日期:2008-06-25
通讯作者: PRAMANIK Surapati
作者简介:PRAMANIK Surapati（1971-），男，印度人，讲师.

Multiobjective Transportation Model with Fuzzy
Parameters: a Priority Based Fuzzy Goal
Programming Approach

PRAMANIK Surapati ¹, ROY Tapan Kumar ²

1 Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, P.O.- Narayanpur, District - North 24 Parganas, West Bengal, India, Pin Code-743126
2 Bengal Engineering and Science University, Shibpur, P.O.- B. Garden, Dist- Howrah, West Bengal, India, Pin-Code-711103

Received:2008-03-06 Revised:2008-04-19 Online:2008-06-25 Published:2008-06-25
Contact: PRAMANIK Surapati

摘要/Abstract

摘要： 针对具有模糊因数的多目标交通问题，提出了一种优先模糊目标规划方法。本文首先建立了模糊目标的隶属度函数，其次，将隶属度函数的最高度作为期望水平并引入了偏差变量，从而将隶属度函数转化为隶属度目标。通过最小化负偏差变量得到最满意解。对模糊目标不同优先级结构下的解进行了敏感性分析，并用欧氏距离函数确定了最佳的目标优先级结构，通过最小化后悔值达到决策区域理想点决策值，得到决策单元最满意解。最后，应用实例对本文方法进行分析验证。

关键词: 模糊目标规划, 模糊数, 隶属函数, 多目标决策, 多目标交通问题

Abstract: This paper presents priority based fuzzy goal programming approach for solving multi-objective transportation problem with fuzzy coefficient. In the model formulation of the problem, the membership functions for the fuzzy goals are defined first. Then the membership functions are transformed into the membership goals by assigning the highest degree (unity) of a membership function as the aspiration level and introducing the deviational variables to each of them. In the solution process, negative deviational variables are minimized to obtain the most satisficing solution. Sensitivity analysis to the solution with the change of priorities of the fuzzy goals is performed. Then the Euclidean distance function is used to identify the appropriate priority structure of the goals and thereby obtaining the most satisficing decision to the decision -making unit by minimizing their regrets of achieving the ideal-point dependent decision in the decision-making context. A numerical example is solved to demonstrate the potential use of proposed approach.

Key words: fuzzy goal programming, fuzzy number, membership function, multi-objective decision making, multi-objective transportation problem

中图分类号:

PRAMANIK Surapati, ROY Tapan Kumar . 基于优先模糊目标规划方法的多目标交通模型研究[J]. 交通运输系统工程与信息, 2008, 8(3): 40-48 .

PRAMANIK Surapati, ROY Tapan Kumar . Multiobjective Transportation Model with Fuzzy
Parameters: a Priority Based Fuzzy Goal
Programming Approach[J]. Journal of Transportation Systems Engineering and Information Technology, 2008, 8(3): 40-48 .

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http://www.tseit.org.cn/CN/Y2008/V8/I3/40

参考文献

[1] Ijiri Y. Management Goals and Accounting for Control[M], Amsterdam: North-Holland Pub., 1965.

[2] Ignizio J P. Goal Programming and Extensions[M], Massachustts: Lexiton, D.C. Health, 1976.

[3] Lee S M. Goal Programming for Decision Analysis[M], Philadelphia: Auerbach Pub., 1972.

[4] Steuer R E. Multiple Criteria Optimization: Theory, Computation and Applications[M], New York: Wiley, 1986.

[5] Hitchcock F L. The distribution of a product from several sources to numerous localities[J]. Journal of Mathematical Physics, 1941, 20(1): 224–230.

[6] Isermann H. The enumeration of all efficient solutions for a linear multi-objective transportation problem[J]. Naval Research Logistic Quarterly, 1979, 26: 123139.

[7] Ringuest J L, Rinks D B. Interactive solutions for the linear multi-objective transportation problem[J]. European Journal of operational Research, 1987, 32(1): 96–106.

[8] Bit A K, Biswal M P, Alam S S. Fuzzy programming approach to multi-criteria decision making transportation problem[J]. Fuzzy Sets and Systems, 1992, 50: 135–141.

[9] Abd El-Wahed, W.F., Lee, S.M. Interactive fuzzy goal programming for multi-objective transportation problems[J]. Omega, 2006, 34(2):158–166.

[10] Gao S P, Liu S A. Two-phase fuzzy algorithms for multi-objective transportation problem[J]. The Journal of Fuzzy Mathematics, 2004, 12(1): 147–155.

[11] Li L, Lai K K. A fuzzy approach to multiobjective transportation problem[J]. Computers and Operations Research, 2000, 27(1): 43–57.

[12] Pramanik S, Roy T K. A fuzzy goal programming technique for solving multi-objective transportation problem[J]. Tamsui Oxford Journal of Management Sciences, 2006, 22(1): 67–89.

[13] Pramanik S, Roy T K. Fuzzy goal programming approach to multilevel programming problems[J]. European Journal of operational Research, 2007, 176(2): 1151–1166.

[14] Zadeh L A. Fuzzy sets. Information and Control, 1965, 8(3): 338–353.

[15] Lee E S, Li R J. Fuzzy multiple objective programming and compromise programming with Pareto optimum[J]. Fuzzy Sets and Systems, 1993, 53(2):275–288.

[16] Yu, P.L. A class of solutions for group decision problems[J]. Management Science, 1973, 19(8): 936–946