基于信息不确定性的军事运输隐蔽性路径的选择问题研究
|
摘要
军用物资在运输道路上的分配问题是国防经济中资源分配的一个重要问题。军事运输在军事物流中处于核心地位,军事物流顺畅与否直接取决于军事运输是否顺利。现代战争规模日益扩大,和平时期非常规突发事件亦频频发生,再加上军事科技的进步使得侦察监视手段和武器装备越来越先进,这些都给军事运输提出了更高的要求。为保证军事运输顺利进行,选择科学合理的军事运输路径是关键,而选择隐蔽程度高的路径是降低不确定信息对军事运输不利影响的直接且有效途径。因此,研究信息不确定条件下军事运输隐蔽性路径的选择问题,对于提高军事运输的水平有着重要意义。
作者首先阐述了军事运输的概念、特点和重要作用,在此基础上归纳出影响军事运输的不确定信息,揭示了不确定信息条件下选择隐蔽的军事运输路径的重要性;其次,针对应急军事运输的特点,构建了军事运输路径隐蔽性评价指标体系,并在此基础上建立基于灰色评价理论的军事运输最大隐蔽性的路径选择模型;再次,为保证战时军事交通流的分配方案有效并且可行,建立了基于容量约束的军事交通路网流量的最大隐蔽性分配模型;接着,为使军事交通流的分配结果更符合实际路况,充分考虑了路长和路宽的路况信息,建立了基于全路况隐蔽性测度的军事交通流分配模型,并且将研究假设从单始点单终点的特殊情况拓展到多始点多终点的一般情况。最后,论文还就军事运输路径隐蔽性评价指标体系和容量约束研究的不足之处,作者提出了有待深入研究的问题。
Military supplies distribution in the transportation on the road is an important issue in the resources allocation of national defense economy. Military transportation occupies a central position in military logistics. Military logistics is smooth or not depends directly on military transportation is smooth or not. The scale of modern warfare is expanding, unconventional emergencies also occur frequently in peacetime, the surveillance means and the weapons become advanced increasingly which due to the progress of military science and technology. All these will give military transportation higher requirements. In order to ensure the smooth progress of military transportation, selecting the military transportation path scientifically and reasonably is the key. Yet selecting high concealment degree path is a direct and effective way to minimize the adverse impact of uncertain information on military transportation. Therefore, studying the problem of military transportation hidden path selection under the condition of information uncertainly has an important significance for improving the level of military transportation.
First, the author described the concept, features and important role of military transportation. And on these bases, summing up uncertain information of military transportation and revealing the importance of selecting the hidden military transportation path under the condition of information uncertainly. Next, it built an evaluation index system of military transportation path concealment according to military transportation features. And on this basis, it built the path selection model of military transportation for the maximum concealment based on grey evaluation theory. Again, in order to ensure the military traffic assignment program effective and feasible in wartime, it built the traffic assignment model of military traffic road-network for the maximum concealment based on capacity constraints. Then, this paper took full account of the road conditions information including the road length and the road width to enable the assignment result of military traffic more in line with the actual road conditions. It built the military traffic assignment model based on the concealment measure of the entire road conditions, and developed the study hypothesis from the special situation which is a single starting point and a single terminal point to the general situation which is multi-starting points and multi- terminal points. Finally, it also proposed the problem to be in-depth studied contrary to the inadequacies of the study on the evaluation index system of military transportation path concealment and capacity constraints.
作者首先阐述了军事运输的概念、特点和重要作用,在此基础上归纳出影响军事运输的不确定信息,揭示了不确定信息条件下选择隐蔽的军事运输路径的重要性;其次,针对应急军事运输的特点,构建了军事运输路径隐蔽性评价指标体系,并在此基础上建立基于灰色评价理论的军事运输最大隐蔽性的路径选择模型;再次,为保证战时军事交通流的分配方案有效并且可行,建立了基于容量约束的军事交通路网流量的最大隐蔽性分配模型;接着,为使军事交通流的分配结果更符合实际路况,充分考虑了路长和路宽的路况信息,建立了基于全路况隐蔽性测度的军事交通流分配模型,并且将研究假设从单始点单终点的特殊情况拓展到多始点多终点的一般情况。最后,论文还就军事运输路径隐蔽性评价指标体系和容量约束研究的不足之处,作者提出了有待深入研究的问题。
Military supplies distribution in the transportation on the road is an important issue in the resources allocation of national defense economy. Military transportation occupies a central position in military logistics. Military logistics is smooth or not depends directly on military transportation is smooth or not. The scale of modern warfare is expanding, unconventional emergencies also occur frequently in peacetime, the surveillance means and the weapons become advanced increasingly which due to the progress of military science and technology. All these will give military transportation higher requirements. In order to ensure the smooth progress of military transportation, selecting the military transportation path scientifically and reasonably is the key. Yet selecting high concealment degree path is a direct and effective way to minimize the adverse impact of uncertain information on military transportation. Therefore, studying the problem of military transportation hidden path selection under the condition of information uncertainly has an important significance for improving the level of military transportation.
First, the author described the concept, features and important role of military transportation. And on these bases, summing up uncertain information of military transportation and revealing the importance of selecting the hidden military transportation path under the condition of information uncertainly. Next, it built an evaluation index system of military transportation path concealment according to military transportation features. And on this basis, it built the path selection model of military transportation for the maximum concealment based on grey evaluation theory. Again, in order to ensure the military traffic assignment program effective and feasible in wartime, it built the traffic assignment model of military traffic road-network for the maximum concealment based on capacity constraints. Then, this paper took full account of the road conditions information including the road length and the road width to enable the assignment result of military traffic more in line with the actual road conditions. It built the military traffic assignment model based on the concealment measure of the entire road conditions, and developed the study hypothesis from the special situation which is a single starting point and a single terminal point to the general situation which is multi-starting points and multi- terminal points. Finally, it also proposed the problem to be in-depth studied contrary to the inadequacies of the study on the evaluation index system of military transportation path concealment and capacity constraints.
引文
[1] Laporte G, Nobert Y. Exact algorithms for the vehicle routing problem [J]. In: Martello S, Laporte G, Minoux M, Ribeiro (Eds.). Surveys in Combinatorial Optimization. Amsterdam: North-Holland, 1987, 147-184
[2]谢金星,刑文训.网络优化[M].北京:清华大学出版社, 2000
[3]苏莹,王英杰,余卓渊.一种建立公交网络的最短路径改进算法[J]地球信息科学, 2005.7(2), 99-104
[4]张振坤.多指标运输问题的数学模型及算法研究[J].郑州大学学报, 2001.33(2), 33-36
[5]段凡丁.关于最短路径的SPFA快速算法[J].西南交通大学学报, 1994.29(2), 207-212
[6]李引珍,顾守淮.铁路网络两顶点间最短路径定向搜索算法[J].铁道学报, 1997.19(2), 25-27
[7]周培德.交通道路网中任意两点间最短路径的快速算法[J].计算机工程, 2002.24 (4), 35-37
[8]李从信,孟祥岗,张颍.GIS超市配送系统开发及路径优化算法研究[J].陕西工学院学报, 2005.21(2), 18-20
[9]王刊良,徐演峰.相异路径选线问题的一种模型与算法[J].系统工程理论方法应用, 2001.10(1), 8-12
[10] Lee CK. A Multiple Path Routing Strategy for Vehicle Route Guidance Systems [J]. Transportation Research, 1994.2C(13), 185-195
[11] Shier R D. On Algorithms for Finding the K Shortest Networks [J]. Paths in a Networks, 1979(919), 195-214
[12] Park D. Multiple Path Based Vehicle Routing in Dynamic and Stochastic Transportation Networks[D] Texas: A&M University, 1998
[13]张国伍.基于节点删除的多路径获取方法的研究[J].北方交通大学学报, 2002.26(2), 77-81
[14]何瑞春,李引珍.最佳相异度相异最短路径的遗传算法[J].兰州交通大学学报(自然科学版), 2002.20 (4), 71-75
[15] Bertsekas D P. Linear Network Optimization: Algorithms and Codes. Massachusetts,Cambridge: MIT Press, 1991
[16] Dantzig, Ramser J. The Truck Dispatching Problem [J]. Management Science, 1959.(6), 80-91
[17] Eilon S, Waston-Gandy C.D.T, Christofides N. Distribution management: Mathematical modeling and practical analysis. London: Griffin, 1991
[18] Christofides N, Mingozzi A, Toth P. State Space Relaxation Procedures for the Computation of Bounds to Routing Problems [J]. Networks, 1981.11, 145-164
[19] Bslinski M, Quandt R. On an Integer Program for a Delivery Problem [J]. Operations Research, 1962.12, 300-304
[20] Clarke G, Wright J W. Scheduling of Vehicles from a Central Depot to a Number of Delivery Points [J]. Operations Research, 1964.12, 568-581
[21] Gillett B, Miller L. A heuristic Algorithm for the Vehicle Dispatch Problem [J]. Operations Research, 1974.22, 340-349
[22]祝崇隽,刘民,吴澄.供应链中车辆路径问题的研究进展及前景[J].计算机集成制造系统—CIMS, 2001.7(11), 1-6
[23] Wark P, Holt J. A Repeated Matching Heuristic for the Vehicle Routing Problem [J]. Operations Research Society, 1994.45 (10), 1156-1167
[24] Stewart W R, Golden B L. Stochastic Vehicle Routing: A Comprehensive Approach [J]. European Journal of Operational Research, 1983.14, 371-385
[25] Laporte G, Louveaux F, Mercure H. Models and Exact Solutions for a Class of Stochastic Location-Routing Problem [J]. European Journal of Operational Research, 1989.39, 71-78
[26] Bouzaiene-Ayari B, Dror M, Laporte G. Vehicle Routing with Stochastic Demands and Split Deliveries [J]. Foundations of Computation and Decision Sciences, 1993.18 (2), 63-69
[27] Teodorovic D, Pavkovic G. The Fuzzy Set Theory a Approach to the Vehicle Routing Problem when Demand at Nodes Is Uncertain [J]. Fuzzy Sets and Systems, 1996.82, 307-317
[28]张得志,凌春雨.多种运输方式的组合优化模型及求解算法[J].长沙铁道学院学报, 2002.20(4), 71-75
[29]李相勇,田澎.带时间窗和随机时间车辆路径问题:模型和算法[J].系统工程理论与实践, 2009.8, 81-90
[30]霍佳震,张磊.有时间窗的集货送货一体化车辆路径规划启发式算法研究[J].物流科技, 2004.5, 64-66
[31]郎茂祥,张炯.有时间窗配送车辆调度问题的禁忌搜索算法[J].北方交通大学学报, 2004.2, 103-110
[32]符卓,聂靖.求解带装载能力限制的开放式车辆路径问题的遗传算法[J].系统工程, 2008.2, 78-83
[33]陈火根,丁红钢,程耀东.物流配送中心车辆调度模型与遗传算法设计[J].浙江大学学报, 2003.5, 513-516
[34]张潜,李钟慎,胡祥培.基于模糊优化的物流配送路径(MLRP)问题研究[J].控制与决策, 2006.6, 689-692
[35]陈韦志.配送中心的运输路径优化研究[D].武汉:武汉理工大学, 2007
[36]孙燕,陈森发,黄鹍.基于灰色评价理论的自适应最优路径选择[J].中国公路学报, 2003.4, 87-90
[37]何胜学,范炳全.基于有效路径的交通流博弈分配算法[J].交通运输系统工程与信息, 2007.2, 115-119
[38]李友好,刘晓佳,施其洲.基于网络的运输通道客运流量分配模型[J].交通运输工程与信息学报, 2005.6, 57-62
[39]李乐园,张小宁,张红军.基于交通瓶颈的动态交通分配模型[J].系统工程理论与实践, 2006.4, 125-129
[40]徐寅峰,武小平,苏兵.基于系统最优策略的占线交通流量分配[J].系统工程, 2009.3, 16-20
[41]许国银,熊孝和,林涛.基于GASA算法的成品燃油战时公路配送路径优化[J].解放军理工大学学报(自然科学版), 2007.2, 180-185
[42]童忠海,方兴.基于Map Basic的战时运输最优路径问题研究[J].国防交通工程与技术, 2007.4, 36-40
[43]郑龙,周经伦,潘正强.基于广义割集算法的军事运输路径优化[J].计算机工程, 2007.6, 4-6,9
[44]石玉峰,门志强.基于模糊多目标决策理论的军事运输路径优化研究[J].交通运输工程与信息学报, 2004.3, 112-116
[45]石玉峰,粟实,彭其渊.基于遗传算法的军事运输路径优化[J].西南交通大学学报, 2005.4, 241-244
[46]石玉峰.具有战时随机损耗的军事运输路径优化[J].系统工程学报, 2005.12, 649-652
[47]石玉峰,彭其渊.一类带有随机模糊损耗的运输路径优化[J].铁道学报, 2005.1, 14-17
[48]石玉峰.战时随机运输时间路径优化研究[J].系统工程理论与实践, 2005.4, 133-136
[49]石玉峰.基于战时模糊运输时间的路径优化[J].交通运输工程与信息学报, 2004.3, 104-107
[50]石玉峰,金建军.战时不确定性运输路径优化[J].空军工程大学学报(自然科学版), 2005.3, 56-59
[51]王进,杨西龙,姜宏刚.遗传算法在军事物流运输路径选择中应用[J].物流技术, 2006.3, 217-219
[52]李岩,戴明强,温林.基于运输风险的战时运输网络交通流分配模型[J].兵工自动化, 2009.2, 22-25
[53]陈建林,陈蓓.战区军事交通运输网络保障能力评价研究[J].铁道运输与经济,2005.5, 78-79
[54]方志耕,龚正,黄西林.公路军事交通运输勤务综合演习项目GERT网络模型研究与分析[J].系统工程理论与实践, 2000.4, 133-135
[55]方志耕,刘思峰,党耀国.最大灰信息熵路网军事交通流最大隐蔽性分配模型研究[J].中国管理科学, 2003.6, 56-61
[56]王宗喜,徐东.军事物流学[M].北京:清华大学出版社, 2007
[57]朱代树,倪滨海.信息化条件下如何确保战时军事交通畅通[J].中国兵工, 2008.6, 54
[58]焦红,吴晓东,王开勇.军事物流系统战时运行环境与不确定因素分析[J].物流技术, 2007.7, 223-225
[59]石玉峰.战时不确定性运输路径优化研究[D].成都:西南交通大学, 2005
[60]吴海兵,王乔.基于多目标模糊决策的炮兵机动最佳路径选择[J].四川兵工学报, 2007.5, 26-30
[61]刘思峰,党耀国,方志耕.灰色系统理论及其应用[M].北京:科学出版社, 2004
[62]李青,朱广训,伞耀.联合作战条件下弹药分配方案优化研究[C].中国运筹学会第七届学术交流会论文集, 2004.10, 1215-1220
[63]李强.公路军事运输线的模糊优选[J].军事运筹与系统工程, 1998.1, 22-25,31
[64]常刚,刘宝新,宋凯.应用灰色评价理论选择最优军事运输方式研究[J].数学的实践与认识, 2007.2, 57-63
[65]龚延成.战时军事物流系统决策理论与方法研究[D].西安:长安大学, 2004
[66]程琳,王炜,王京元等.城市道路网络容量、交通规划和交通管理[J].公路交通科技, 2005.7, 118-122
[67]方志耕,刘思峰,陆芳等.区间灰数表征与算法改进及其GM(1,1)模型应用研究[J].中国工程科学, 2005.2, 57-61
[68]邱菀华.管理决策与应用熵学[M].北京:机械工业出版社.2001, 146,358-364
[69]曾运清,王春颖,周德荣.熵权值——模糊综合评价法在陆路国防交通网络评价研究中应用[J].军事交通学院学报, 2007. 4 , 62-63
[70]陈冬华.结构熵在交通运输网研究中的应用[J].交通标准化, 2008.6, 176-178
[2]谢金星,刑文训.网络优化[M].北京:清华大学出版社, 2000
[3]苏莹,王英杰,余卓渊.一种建立公交网络的最短路径改进算法[J]地球信息科学, 2005.7(2), 99-104
[4]张振坤.多指标运输问题的数学模型及算法研究[J].郑州大学学报, 2001.33(2), 33-36
[5]段凡丁.关于最短路径的SPFA快速算法[J].西南交通大学学报, 1994.29(2), 207-212
[6]李引珍,顾守淮.铁路网络两顶点间最短路径定向搜索算法[J].铁道学报, 1997.19(2), 25-27
[7]周培德.交通道路网中任意两点间最短路径的快速算法[J].计算机工程, 2002.24 (4), 35-37
[8]李从信,孟祥岗,张颍.GIS超市配送系统开发及路径优化算法研究[J].陕西工学院学报, 2005.21(2), 18-20
[9]王刊良,徐演峰.相异路径选线问题的一种模型与算法[J].系统工程理论方法应用, 2001.10(1), 8-12
[10] Lee CK. A Multiple Path Routing Strategy for Vehicle Route Guidance Systems [J]. Transportation Research, 1994.2C(13), 185-195
[11] Shier R D. On Algorithms for Finding the K Shortest Networks [J]. Paths in a Networks, 1979(919), 195-214
[12] Park D. Multiple Path Based Vehicle Routing in Dynamic and Stochastic Transportation Networks[D] Texas: A&M University, 1998
[13]张国伍.基于节点删除的多路径获取方法的研究[J].北方交通大学学报, 2002.26(2), 77-81
[14]何瑞春,李引珍.最佳相异度相异最短路径的遗传算法[J].兰州交通大学学报(自然科学版), 2002.20 (4), 71-75
[15] Bertsekas D P. Linear Network Optimization: Algorithms and Codes. Massachusetts,Cambridge: MIT Press, 1991
[16] Dantzig, Ramser J. The Truck Dispatching Problem [J]. Management Science, 1959.(6), 80-91
[17] Eilon S, Waston-Gandy C.D.T, Christofides N. Distribution management: Mathematical modeling and practical analysis. London: Griffin, 1991
[18] Christofides N, Mingozzi A, Toth P. State Space Relaxation Procedures for the Computation of Bounds to Routing Problems [J]. Networks, 1981.11, 145-164
[19] Bslinski M, Quandt R. On an Integer Program for a Delivery Problem [J]. Operations Research, 1962.12, 300-304
[20] Clarke G, Wright J W. Scheduling of Vehicles from a Central Depot to a Number of Delivery Points [J]. Operations Research, 1964.12, 568-581
[21] Gillett B, Miller L. A heuristic Algorithm for the Vehicle Dispatch Problem [J]. Operations Research, 1974.22, 340-349
[22]祝崇隽,刘民,吴澄.供应链中车辆路径问题的研究进展及前景[J].计算机集成制造系统—CIMS, 2001.7(11), 1-6
[23] Wark P, Holt J. A Repeated Matching Heuristic for the Vehicle Routing Problem [J]. Operations Research Society, 1994.45 (10), 1156-1167
[24] Stewart W R, Golden B L. Stochastic Vehicle Routing: A Comprehensive Approach [J]. European Journal of Operational Research, 1983.14, 371-385
[25] Laporte G, Louveaux F, Mercure H. Models and Exact Solutions for a Class of Stochastic Location-Routing Problem [J]. European Journal of Operational Research, 1989.39, 71-78
[26] Bouzaiene-Ayari B, Dror M, Laporte G. Vehicle Routing with Stochastic Demands and Split Deliveries [J]. Foundations of Computation and Decision Sciences, 1993.18 (2), 63-69
[27] Teodorovic D, Pavkovic G. The Fuzzy Set Theory a Approach to the Vehicle Routing Problem when Demand at Nodes Is Uncertain [J]. Fuzzy Sets and Systems, 1996.82, 307-317
[28]张得志,凌春雨.多种运输方式的组合优化模型及求解算法[J].长沙铁道学院学报, 2002.20(4), 71-75
[29]李相勇,田澎.带时间窗和随机时间车辆路径问题:模型和算法[J].系统工程理论与实践, 2009.8, 81-90
[30]霍佳震,张磊.有时间窗的集货送货一体化车辆路径规划启发式算法研究[J].物流科技, 2004.5, 64-66
[31]郎茂祥,张炯.有时间窗配送车辆调度问题的禁忌搜索算法[J].北方交通大学学报, 2004.2, 103-110
[32]符卓,聂靖.求解带装载能力限制的开放式车辆路径问题的遗传算法[J].系统工程, 2008.2, 78-83
[33]陈火根,丁红钢,程耀东.物流配送中心车辆调度模型与遗传算法设计[J].浙江大学学报, 2003.5, 513-516
[34]张潜,李钟慎,胡祥培.基于模糊优化的物流配送路径(MLRP)问题研究[J].控制与决策, 2006.6, 689-692
[35]陈韦志.配送中心的运输路径优化研究[D].武汉:武汉理工大学, 2007
[36]孙燕,陈森发,黄鹍.基于灰色评价理论的自适应最优路径选择[J].中国公路学报, 2003.4, 87-90
[37]何胜学,范炳全.基于有效路径的交通流博弈分配算法[J].交通运输系统工程与信息, 2007.2, 115-119
[38]李友好,刘晓佳,施其洲.基于网络的运输通道客运流量分配模型[J].交通运输工程与信息学报, 2005.6, 57-62
[39]李乐园,张小宁,张红军.基于交通瓶颈的动态交通分配模型[J].系统工程理论与实践, 2006.4, 125-129
[40]徐寅峰,武小平,苏兵.基于系统最优策略的占线交通流量分配[J].系统工程, 2009.3, 16-20
[41]许国银,熊孝和,林涛.基于GASA算法的成品燃油战时公路配送路径优化[J].解放军理工大学学报(自然科学版), 2007.2, 180-185
[42]童忠海,方兴.基于Map Basic的战时运输最优路径问题研究[J].国防交通工程与技术, 2007.4, 36-40
[43]郑龙,周经伦,潘正强.基于广义割集算法的军事运输路径优化[J].计算机工程, 2007.6, 4-6,9
[44]石玉峰,门志强.基于模糊多目标决策理论的军事运输路径优化研究[J].交通运输工程与信息学报, 2004.3, 112-116
[45]石玉峰,粟实,彭其渊.基于遗传算法的军事运输路径优化[J].西南交通大学学报, 2005.4, 241-244
[46]石玉峰.具有战时随机损耗的军事运输路径优化[J].系统工程学报, 2005.12, 649-652
[47]石玉峰,彭其渊.一类带有随机模糊损耗的运输路径优化[J].铁道学报, 2005.1, 14-17
[48]石玉峰.战时随机运输时间路径优化研究[J].系统工程理论与实践, 2005.4, 133-136
[49]石玉峰.基于战时模糊运输时间的路径优化[J].交通运输工程与信息学报, 2004.3, 104-107
[50]石玉峰,金建军.战时不确定性运输路径优化[J].空军工程大学学报(自然科学版), 2005.3, 56-59
[51]王进,杨西龙,姜宏刚.遗传算法在军事物流运输路径选择中应用[J].物流技术, 2006.3, 217-219
[52]李岩,戴明强,温林.基于运输风险的战时运输网络交通流分配模型[J].兵工自动化, 2009.2, 22-25
[53]陈建林,陈蓓.战区军事交通运输网络保障能力评价研究[J].铁道运输与经济,2005.5, 78-79
[54]方志耕,龚正,黄西林.公路军事交通运输勤务综合演习项目GERT网络模型研究与分析[J].系统工程理论与实践, 2000.4, 133-135
[55]方志耕,刘思峰,党耀国.最大灰信息熵路网军事交通流最大隐蔽性分配模型研究[J].中国管理科学, 2003.6, 56-61
[56]王宗喜,徐东.军事物流学[M].北京:清华大学出版社, 2007
[57]朱代树,倪滨海.信息化条件下如何确保战时军事交通畅通[J].中国兵工, 2008.6, 54
[58]焦红,吴晓东,王开勇.军事物流系统战时运行环境与不确定因素分析[J].物流技术, 2007.7, 223-225
[59]石玉峰.战时不确定性运输路径优化研究[D].成都:西南交通大学, 2005
[60]吴海兵,王乔.基于多目标模糊决策的炮兵机动最佳路径选择[J].四川兵工学报, 2007.5, 26-30
[61]刘思峰,党耀国,方志耕.灰色系统理论及其应用[M].北京:科学出版社, 2004
[62]李青,朱广训,伞耀.联合作战条件下弹药分配方案优化研究[C].中国运筹学会第七届学术交流会论文集, 2004.10, 1215-1220
[63]李强.公路军事运输线的模糊优选[J].军事运筹与系统工程, 1998.1, 22-25,31
[64]常刚,刘宝新,宋凯.应用灰色评价理论选择最优军事运输方式研究[J].数学的实践与认识, 2007.2, 57-63
[65]龚延成.战时军事物流系统决策理论与方法研究[D].西安:长安大学, 2004
[66]程琳,王炜,王京元等.城市道路网络容量、交通规划和交通管理[J].公路交通科技, 2005.7, 118-122
[67]方志耕,刘思峰,陆芳等.区间灰数表征与算法改进及其GM(1,1)模型应用研究[J].中国工程科学, 2005.2, 57-61
[68]邱菀华.管理决策与应用熵学[M].北京:机械工业出版社.2001, 146,358-364
[69]曾运清,王春颖,周德荣.熵权值——模糊综合评价法在陆路国防交通网络评价研究中应用[J].军事交通学院学报, 2007. 4 , 62-63
[70]陈冬华.结构熵在交通运输网研究中的应用[J].交通标准化, 2008.6, 176-178