区间值最小二乘核仁解及在供应链合作利益分配中的应用

doi:10.16381/j.cnki.issn1003-207x.2017.12.009

中国管理科学 ›› 2017, Vol. 25 ›› Issue (12): 78-87.doi: 10.16381/j.cnki.issn1003-207x.2017.12.009

区间值最小二乘核仁解及在供应链合作利益分配中的应用

刘家财^1,2, 李登峰¹, 胡勋锋¹

1. 福州大学经济与管理学院工商管理研究院, 福建福州 350116;
2. 福建农林大学交通与土木工程学院, 福建福州 350002

收稿日期:2016-04-15 修回日期:2016-09-24 出版日期:2017-12-20 发布日期:2018-02-10
通讯作者: 李登峰(1965-),男(汉族),广西博白人,福州大学经济与管理学院,教授,博导,研究方向:经济管理决策与对策(博弈),E-mail:lidengfeng@fzu.edu.cn E-mail:lidengfeng@fzu.edu.cn
基金资助:
国家自然科学基金重点资助项目（71231003）；国家自然科学基金资助项目（71171055）；福建省软科学研究计划项目（2016R0012）；福建省社会科学规划项目（2013C024）；福建省中青年教师教育科研项目（JA13122）；福建农林大学高水平大学建设重点资助项目（113-612014018）

Interval-Valued Least Square Nucleolus and Its Application in Cooperative Profit Allocation of Supply Chain

LIU Jia-cai^1,2, LI Deng-feng¹, HU Xun-feng¹

1. Institute of Business Administration, School of Economics and Management, Fuzhou University, Fuzhou 350116, China;
2. School of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350002, China

Received:2016-04-15 Revised:2016-09-24 Online:2017-12-20 Published:2018-02-10

摘要/Abstract

摘要： 针对合作对策中联盟值（或特征函数）常表示为区间值而非实数的现象，提出两种新的二次规划求解方法，该方法能快速、有效的获得n人区间值合作对策的区间值最小二乘预核仁解和核仁解。首先，利用反映联盟不满意度的平方超量e（S，x）=（υ_L（S）-x_L（S））²+（υ_R（S）-x_R（S））²，构建求解区间值最小二乘预核仁解的二次规划模型，据此确定每个局中人的区间值分配x_i^E*=[x_Li^E*，x_Ri^E*]（i∈N）。其中，x_Li^E*=（υ_L（N））/n+1/（n2^n-2）（na_Li（υ）-???20171209???a_Lj（υ）），x_Ri^E*=（υ_R（N））/n+1/（n2^n-2）（na_Ri（υ）-???20171209???a_Rj（υ））（i∈N）。接着，考虑个体合理性，拓展所导出的数学优化模型，获得区间值最小二乘核仁解。然后，讨论最小二乘预核仁解和核仁解的一些重要性质，如，存在性和唯一性、有效性、可加性、对称性、匿名性，等。最后，利用供应链合作利益分配的数学算例验证所提出的二次规划模型和方法的合理性、有效性和优越性。

关键词: 模糊对策, 合作对策, 区间值, 平方超量, 核仁

Abstract: Due to the character that values (or characteristic functions) of coalitions of players are usually expressed with intervals rather than real numbers in real situations, two quadratic programming methods are proposed, which can quickly and effectively compute n-person interval-valued least square prenucleolus and nucleolus of interval-valued cooperative games. In this methodology, based on the square excess e(S,x)=(υ_L(S)-x_L(S))²+(υ_R(S)-x_R(S))² which can be interpreted as a measure of the dissatisfaction of the coalitions, the quadratic programming model is firstly constructed for interval-valued least square prenucleolus of interval-valued cooperative games and obtain players' interval-valued imputations x_i^E*=[x_Li^E*,x_Ri^E*](i∈N), where x_Li^E*=(υ_L(N))/n+1/(n2^n-2)(na_Li(υ)-???20171209???a_Lj(υ)),x_Ri^E*=(υ_R(N))/n+1/(n2^n-2)(na_Ri(υ)-???20171209???a_Rj(υ))(i∈N). Then, taking into account the individual rationality, the aforementioned optimization mathematical model is extended and all players' interval-valued least square nucleolus is solued. Moreover, some useful properties of the interval-valued least square prenucleolus and nucleolus are discussed,such as existence and uniqueness, efficiency, additivity, symmetry, and anonymity. Finally, the quadratic programming models and methods are illustrated with a numerical example about the optimal profit allocation of supply chain and the computational result is analyzed to show the validity, applicability, and advantages.

Key words: fuzzy game, cooperative game, interval, square Excess, nucleolus

中图分类号:

O225

刘家财, 李登峰, 胡勋锋. 区间值最小二乘核仁解及在供应链合作利益分配中的应用[J]. 中国管理科学, 2017, 25(12): 78-87.

LIU Jia-cai, LI Deng-feng, HU Xun-feng. Interval-Valued Least Square Nucleolus and Its Application in Cooperative Profit Allocation of Supply Chain[J]. Chinese Journal of Management Science, 2017, 25(12): 78-87.

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区间值最小二乘核仁解及在供应链合作利益分配中的应用

Interval-Valued Least Square Nucleolus and Its Application in Cooperative Profit Allocation of Supply Chain

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