| 区间合作对策核心存在性的进一步讨论 |
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| 引用本文： | 关菲,栗军.区间合作对策核心存在性的进一步讨论[J].运筹与管理,2018,27(4):10-14. |
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| 作者姓名： | 关菲 栗军 |
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| 作者单位： | 1.河北经贸大学 数学与统计学学院,河北 石家庄 050061; 2.国网石家庄供电分公司,河北 石家庄 050000 |
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| 基金项目： | 河北省自然科学基金资助项目(F2017207010);河北省高等学校科学技术研究项目(QN2017060);国家自然科学基金项目(71371030);河北经贸大学校内科研基金青年项目(2017KYQ07)资助 |
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| 摘 要： | 区间合作对策,是研究当联盟收益值为区间数情形时如何进行合理收益分配的数学模型。近年来,其解的存在性与合理性等问题引起了国内外专家的广泛关注。区间核心,是区间合作对策中一个非常稳定的集值解概念。本文首先针对区间核心的存在性进行深入的讨论,通过引入强非均衡,极小强均衡,模单调等概念,从不同角度给出判别区间核心存在性的充分条件。其次,通过引入相关参数,定义了广义区间核心,并给出定理讨论了区间核心与广义区间核心的存在关系。本文的结论将为进一步推动区间合作对策的发展,为解决区间不确定情形下的收益分配问题奠定理论基础。
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| 关 键 词： | 区间合作对策 区间核心 均衡对策 极小强均衡 广义区间核心 |
| 收稿时间： | 2017-08-31 |
A Further Discussion on the Existence of Interval Core |
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| GUAN Fei,LI Jun.A Further Discussion on the Existence of Interval Core[J].Operations Research and Management Science,2018,27(4):10-14. |
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| Authors: | GUAN Fei LI Jun |
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| Affiliation: | 1.College of Mathematics & Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China; 2.State Grid Shijiazhuang Electric Power Supply Company, Shijiazhuang 050000, China |
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| Abstract: | Interval cooperative game is a kind of model focusing on how to allocate the profits reasonably when the profits of any coalition are interval numbers. For the past years, the existence and reasonableness of its solutions have aroused widespread concern. Interval core is a stable set-valued solution concept in interval cooperative game. Thus in this paper, we firstly have a further discussion on the existence of interval core by introducing some concepts such as: strongly unbalanced, minimal strongly balanced, size monotonic and so on. Then on the condition that the interval profit value of any coalition is not fully used to allocate, a generalized interval cooperative game and its solution concepts, such as generalized interval imputation, generalized interval core are proposed, a theorem to discuss the existence of generalized interval core is developed. The conclusions in this paper will promote the development of interval cooperative games and lay a sound base for solving the profit allocation problems under interval uncertainties. |
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| Keywords: | interval cooperative games interval core balanced games minimal strongly balanced generalized interval core1 |
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