柔性决策
摘要
在一个决策中，如果决策者是有限理性的，而且决策者的愿望和偏好、决策问题的
约束条件和(或)决策目标是柔性的，那么就称这样的决策为柔性决策。本文提出了符
合客观决策问题的柔性决策的概念，并把柔性决策的思想贯穿于三方面问题的研究，即
多目标决策问题、资源分配问题和一类合作协商对策问题．为解决柔性决策问题，本文
采用了maximin方法、集包含方法、交互式方法和区间分析方法。
为解决多目标柔性决策问题，本文设计了交互式的maximin方法。尽管以前人们
也应用这种方法，但并没有考虑如何根据决策者的愿望和偏好调整满意解。而事实上如
果不按照一定的规律进行调整，就不能保证所求出的新解符合决策者的要求。因此，本
文对调整原理进行了研究，所提出的交互式maximin方法能够满足决策要求，适合于
柔性决策问题。本文还把交互式的maximin方法同集包含方法和区间分析方法结合起
来，用以解决线性的和一些非线性的多目标柔性决策问题．
资源分配问题也是多目标柔性决策问题，同时，这种决策问题中具有多个决策者，
包括一个上级决策者和多个下级部门决策者，上级决策者要根据下级决策者汇报的信
息，采用大系统分解协调技术确定如何把资源分配到下级部门．为解决这样的问题，本
文提出的柔性决策方法把大系统分解协调方法和激励控制方法结合起来，这种方法包括
以下两部分内容：
1． 多目标柔性决策的maximin方法。人们已提出了一些求解maximin(或
minimax)规划的算法，这些算法要求规划问题无约束或具有线性约束，以及要求有关
函数的二次微分信息．但在资源分配问题中，约束可能是非线性的，上级决策者最多能
得到有关函数的一次微分信息．因此，本文根据资源分配问题的特点，设计了适合于应
用分解协调技术的逐点线性化迭代算法，并证明了算法的收敛性．
2． 引导下级汇报真实信息的激励策略．尽管人们提出了一些资源分配问题中的激
励策略，但不符合管理科学的基本原则，在实际中行不通．为此，本文从我国具体情况
出发，提出了“承包机制”的激励策略，这种策略对真实信息是ε-可诱导的，也是鼓励
下级努力工作的策略，适用于柔性决策问题，符合实际情况，克服了其它策略的种种缺
陷．
本文还针对一类合作对策问题研究了合作对策的协商对策方法．由于在合作对策问
题中，对决策者合作行为的约束是柔性的，决策者的愿望也是柔性的，因此合作对策问
题是柔性决策问题．针对这一类合作对策问题，本文提出了协商对策的maximin．柔性
决策方法，根据这种方法求出的解具有公平性和有效性，符合管理科学的基本原则；在
一定的条件下，这种解也是字典序极大极小解．
本文最后对全文的工作做了总结，并对今后的研究方向进行了展望．
A decision is defined to be flexible decision if (1) the Decision Maker (DM) has bounded rationality, and (2) the preference of the DM, the constraints of the decision problem, and/or the goals the DM seeks for are flexible. The motif of this paper is flexible decision which accords with reality. Based on the concept of flexible decision, this paper studies 3 problems. They are multiobjective decision making, resource allocation and one kind of cooperative game. In order to solve the flexible decision problem, the methods used in this paper include maximin method, set inclusion method, interactive method and interval analysis method.
In order to solve the multiobjective flexible decision problem, this paper presents the interactive maximin method. Though the method is used by others, it remains unsolved about how to adjust satisfying solution according to DM's preference. In fact, the adjusted solution may be not in agreement with DM's requirement if some rules are not applied. So this paper studies the principles of adjustment, and gives the interactive maximin method suitable for flexible decision making. The set inclusion method and interval analysis method are integrated with the interactive maximin method to solve linear and some nonlinear flexible decision problems.
The resource allocation problem is multiobjective flexible decision problem. And this kind of decision problem consists many DMs, including one leader DM and many follower DMs. The leader DM uses the technique of large scale system decomposition and coordination to look for allocation scheme according to the information provided by follower DMs. To solve this kind of decision problem, this paper presents the flexible decision method that cooperates large scale system decomposition, coordination and incentive control. This method consists of two parts as follows:
(1) The maximin method of multiobjective flexible decision. There are many existing algorithms that solve the maximin or minimax programming without constraint or with linear constraints. Some of the algorithms need the 2nd order differential information of objective functions. In resource allocation problem, however, the constraints may be nonlinear, the leader DM can only get the 1st order differential information of the functions. So, according to the characteristics of resource allocation problem, this paper gives the iterating algorithm by means of piecewise linearization. The algorithm is proved to be convergent.
(2) Incentive control that induces the follower DMs to tell the truth. Although some incentive strategies in resource allocation problem are given by other researchers, the strategies are not in keeping with the basic principles of management science, and can not be applied to real problem. According to the real situation of China, this paper designs "Contract Mechanism" (CM) which is - inducible for the true information and encourage follower DMs to work hard. As the incentive strategy, the CM overcomes the disadvantages that other strategies have and is suitable for flexible decision problem.
This paper also studies the bargaining method for one kind of cooperative game. In the cooperative game, the constraint of DMs' cooperative behavior is flexible, the preferences of DMs are flexible. Thus the problem is the flexible decision problem. The flexible decision method of bargaining for the kind of cooperative game is presented. The solution by the method is egalitarian and efficient. Under some condition, it is the lexicographic maximin solution.
At the end of the paper, a summary is made, the future research development is discussed
约束条件和(或)决策目标是柔性的，那么就称这样的决策为柔性决策。本文提出了符
合客观决策问题的柔性决策的概念，并把柔性决策的思想贯穿于三方面问题的研究，即
多目标决策问题、资源分配问题和一类合作协商对策问题．为解决柔性决策问题，本文
采用了maximin方法、集包含方法、交互式方法和区间分析方法。
为解决多目标柔性决策问题，本文设计了交互式的maximin方法。尽管以前人们
也应用这种方法，但并没有考虑如何根据决策者的愿望和偏好调整满意解。而事实上如
果不按照一定的规律进行调整，就不能保证所求出的新解符合决策者的要求。因此，本
文对调整原理进行了研究，所提出的交互式maximin方法能够满足决策要求，适合于
柔性决策问题。本文还把交互式的maximin方法同集包含方法和区间分析方法结合起
来，用以解决线性的和一些非线性的多目标柔性决策问题．
资源分配问题也是多目标柔性决策问题，同时，这种决策问题中具有多个决策者，
包括一个上级决策者和多个下级部门决策者，上级决策者要根据下级决策者汇报的信
息，采用大系统分解协调技术确定如何把资源分配到下级部门．为解决这样的问题，本
文提出的柔性决策方法把大系统分解协调方法和激励控制方法结合起来，这种方法包括
以下两部分内容：
1． 多目标柔性决策的maximin方法。人们已提出了一些求解maximin(或
minimax)规划的算法，这些算法要求规划问题无约束或具有线性约束，以及要求有关
函数的二次微分信息．但在资源分配问题中，约束可能是非线性的，上级决策者最多能
得到有关函数的一次微分信息．因此，本文根据资源分配问题的特点，设计了适合于应
用分解协调技术的逐点线性化迭代算法，并证明了算法的收敛性．
2． 引导下级汇报真实信息的激励策略．尽管人们提出了一些资源分配问题中的激
励策略，但不符合管理科学的基本原则，在实际中行不通．为此，本文从我国具体情况
出发，提出了“承包机制”的激励策略，这种策略对真实信息是ε-可诱导的，也是鼓励
下级努力工作的策略，适用于柔性决策问题，符合实际情况，克服了其它策略的种种缺
陷．
本文还针对一类合作对策问题研究了合作对策的协商对策方法．由于在合作对策问
题中，对决策者合作行为的约束是柔性的，决策者的愿望也是柔性的，因此合作对策问
题是柔性决策问题．针对这一类合作对策问题，本文提出了协商对策的maximin．柔性
决策方法，根据这种方法求出的解具有公平性和有效性，符合管理科学的基本原则；在
一定的条件下，这种解也是字典序极大极小解．
本文最后对全文的工作做了总结，并对今后的研究方向进行了展望．
A decision is defined to be flexible decision if (1) the Decision Maker (DM) has bounded rationality, and (2) the preference of the DM, the constraints of the decision problem, and/or the goals the DM seeks for are flexible. The motif of this paper is flexible decision which accords with reality. Based on the concept of flexible decision, this paper studies 3 problems. They are multiobjective decision making, resource allocation and one kind of cooperative game. In order to solve the flexible decision problem, the methods used in this paper include maximin method, set inclusion method, interactive method and interval analysis method.
In order to solve the multiobjective flexible decision problem, this paper presents the interactive maximin method. Though the method is used by others, it remains unsolved about how to adjust satisfying solution according to DM's preference. In fact, the adjusted solution may be not in agreement with DM's requirement if some rules are not applied. So this paper studies the principles of adjustment, and gives the interactive maximin method suitable for flexible decision making. The set inclusion method and interval analysis method are integrated with the interactive maximin method to solve linear and some nonlinear flexible decision problems.
The resource allocation problem is multiobjective flexible decision problem. And this kind of decision problem consists many DMs, including one leader DM and many follower DMs. The leader DM uses the technique of large scale system decomposition and coordination to look for allocation scheme according to the information provided by follower DMs. To solve this kind of decision problem, this paper presents the flexible decision method that cooperates large scale system decomposition, coordination and incentive control. This method consists of two parts as follows:
(1) The maximin method of multiobjective flexible decision. There are many existing algorithms that solve the maximin or minimax programming without constraint or with linear constraints. Some of the algorithms need the 2nd order differential information of objective functions. In resource allocation problem, however, the constraints may be nonlinear, the leader DM can only get the 1st order differential information of the functions. So, according to the characteristics of resource allocation problem, this paper gives the iterating algorithm by means of piecewise linearization. The algorithm is proved to be convergent.
(2) Incentive control that induces the follower DMs to tell the truth. Although some incentive strategies in resource allocation problem are given by other researchers, the strategies are not in keeping with the basic principles of management science, and can not be applied to real problem. According to the real situation of China, this paper designs "Contract Mechanism" (CM) which is - inducible for the true information and encourage follower DMs to work hard. As the incentive strategy, the CM overcomes the disadvantages that other strategies have and is suitable for flexible decision problem.
This paper also studies the bargaining method for one kind of cooperative game. In the cooperative game, the constraint of DMs' cooperative behavior is flexible, the preferences of DMs are flexible. Thus the problem is the flexible decision problem. The flexible decision method of bargaining for the kind of cooperative game is presented. The solution by the method is egalitarian and efficient. Under some condition, it is the lexicographic maximin solution.
At the end of the paper, a summary is made, the future research development is discussed
引文
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93． Zheng Weiming and Shi Yongheng. (1989a), Decision in flexible environment, The bulletin of the vocational section Nr. 15, The 10th scientific conference of VUT Brno.
94． Zheng Weiming and Shi Yongheng (1989b), Some properties of maximin operator in flexible optimization, The 10th international conference on systems
science, Wroclaw, Polland.
95． Zheng, Y. P., Basar, T. and Cruz, J. B. (1984) , Stackelberg strategies and incentives in multi-person deterministic decision problems, IEEE trans, on Systems, Man, and Cybernetics, SMC-14, 10-24．
96． Zimmermann, H.-J. (1978) , Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems 1, 44-55．
97 Zimmermann, H.-J. (1983) , Fuzzy mathematical programming, Computers and operations research 10, 291-298．
98 Zionts, S. (1981) , A multiple criteria method for choosing among discrete alternatives, European journal of operational research 7, 143-147．
99 Ziphin, P. H. (1980) , Simple ranking methods for allocation of one resource, Management sciences 26, 34-43．
100． Oil & Energy Trends: Monthly Analysis and Statistics, June-September, 1989．
101 Petroleum Economist, Sep., 1988-Feb., 1989．
102 Petroleum Supply and Demand, Sep., 1988-Feb., 1989．
103 Statistical Year Book, 1978-1988．
104 Statistics Yearbook, 1978-1988．
105 费根鲍姆，麦科达克(1985) ，第五代-日本第五代电脑对世界的冲击，中国友谊 出版公司．
106． 黄正夏(1984) ，坚持改革，全力推行“三全面”分层经营承包责任制，经济管理 8，39-42，16．
107． 孔茨，奥唐奈，韦里克(1987) ，管理学，中国社会科学出版社．
108． 厉以宁(1986) ，体制·目标·人-经济学面临的挑战，黑龙江人民出版社．
109． 厉以宁，秦宛顺(1983) ，现代西方经济学概论，北京大学出版社．
110． 尼尔逊(1984) ，人工智能原理，科学出版社．
111． 曲晓飞(1990) 。协商对策理论的发展，系统工程，vo1． 8，No．4，44-49．
112． 石永恒(1987) ，柔性环境中的决策，硕士论文，清华大学，自动化系．
113． 石永恒(1989) ，离散系统中的柔性决策方法，清华大学研究生学报，第3期， 112-116．
114． 石永恒，柔性环境中的决策，即将发表于<系统工程理论与实践>，1991年第1 期。
115． 石永恒，郑维敏，壬永县(1987) ，柔性环境中的决策支持系统及其在扶贫规划 中的应用．农业系统工程会议论文，庐山．
116． 王金德(1984) ，随机规划简介，运筹学杂志，vol．3，．No．1．
117． 汪培庄(1984) ，模糊集合论及其应用，上海科学技术出版社．
118 西蒙(1982) ，管理决策新科学，中国社会科学出版社．
119． 西蒙(1989) ，现代决策理论的基石，北京经济学院出版社．
120． 席少霖，赵风治(1983) ，最优化计算方法，上海科学技术出版社．
121． 徐国华，赵平(1989) ，管理学，清华大学出版社．
122． 叶光(1987) ，石油战略的狂飙，国际贸易，vol．1，27-30．
123 章志光(1985) ．心理学，人民教育出版社．
124 郑维敏(1986) ，系统工程FORTRAN程序集，清华大学出版社．
125 郑维敏，宋安澜(1988) ，带不确定因素的多目标决策分析(研究报告)，清华大 学经济管理学院．
126 郑应平(1985) ．多人多级递阶决策的几个问题-鼓励性对策及模型简化，自动化 学报，vol．11． No．4，372-378．
127 郑应平(1987) ．多人决策与博弈论(一)-(六)，信息与控制，vol．1-vol．6．
128 中共抚州市委办公室调研室(1984) ，企业承包中的几个问题，经济管理7， 38-40．
129 世界经济年鉴，1978-1989．
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science, Wroclaw, Polland.
95． Zheng, Y. P., Basar, T. and Cruz, J. B. (1984) , Stackelberg strategies and incentives in multi-person deterministic decision problems, IEEE trans, on Systems, Man, and Cybernetics, SMC-14, 10-24．
96． Zimmermann, H.-J. (1978) , Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems 1, 44-55．
97 Zimmermann, H.-J. (1983) , Fuzzy mathematical programming, Computers and operations research 10, 291-298．
98 Zionts, S. (1981) , A multiple criteria method for choosing among discrete alternatives, European journal of operational research 7, 143-147．
99 Ziphin, P. H. (1980) , Simple ranking methods for allocation of one resource, Management sciences 26, 34-43．
100． Oil & Energy Trends: Monthly Analysis and Statistics, June-September, 1989．
101 Petroleum Economist, Sep., 1988-Feb., 1989．
102 Petroleum Supply and Demand, Sep., 1988-Feb., 1989．
103 Statistical Year Book, 1978-1988．
104 Statistics Yearbook, 1978-1988．
105 费根鲍姆，麦科达克(1985) ，第五代-日本第五代电脑对世界的冲击，中国友谊 出版公司．
106． 黄正夏(1984) ，坚持改革，全力推行“三全面”分层经营承包责任制，经济管理 8，39-42，16．
107． 孔茨，奥唐奈，韦里克(1987) ，管理学，中国社会科学出版社．
108． 厉以宁(1986) ，体制·目标·人-经济学面临的挑战，黑龙江人民出版社．
109． 厉以宁，秦宛顺(1983) ，现代西方经济学概论，北京大学出版社．
110． 尼尔逊(1984) ，人工智能原理，科学出版社．
111． 曲晓飞(1990) 。协商对策理论的发展，系统工程，vo1． 8，No．4，44-49．
112． 石永恒(1987) ，柔性环境中的决策，硕士论文，清华大学，自动化系．
113． 石永恒(1989) ，离散系统中的柔性决策方法，清华大学研究生学报，第3期， 112-116．
114． 石永恒，柔性环境中的决策，即将发表于<系统工程理论与实践>，1991年第1 期。
115． 石永恒，郑维敏，壬永县(1987) ，柔性环境中的决策支持系统及其在扶贫规划 中的应用．农业系统工程会议论文，庐山．
116． 王金德(1984) ，随机规划简介，运筹学杂志，vol．3，．No．1．
117． 汪培庄(1984) ，模糊集合论及其应用，上海科学技术出版社．
118 西蒙(1982) ，管理决策新科学，中国社会科学出版社．
119． 西蒙(1989) ，现代决策理论的基石，北京经济学院出版社．
120． 席少霖，赵风治(1983) ，最优化计算方法，上海科学技术出版社．
121． 徐国华，赵平(1989) ，管理学，清华大学出版社．
122． 叶光(1987) ，石油战略的狂飙，国际贸易，vol．1，27-30．
123 章志光(1985) ．心理学，人民教育出版社．
124 郑维敏(1986) ，系统工程FORTRAN程序集，清华大学出版社．
125 郑维敏，宋安澜(1988) ，带不确定因素的多目标决策分析(研究报告)，清华大 学经济管理学院．
126 郑应平(1985) ．多人多级递阶决策的几个问题-鼓励性对策及模型简化，自动化 学报，vol．11． No．4，372-378．
127 郑应平(1987) ．多人决策与博弈论(一)-(六)，信息与控制，vol．1-vol．6．
128 中共抚州市委办公室调研室(1984) ，企业承包中的几个问题，经济管理7， 38-40．
129 世界经济年鉴，1978-1989．