运筹与管理2017，Vol.26Issue(10)：1-9,9.DOI:10.12005/orms.2017.0227
区间值合作对策的广义区间Shapley值
Generalized Interval Shapley Value for Interval-valued Cooperative Games
摘要
Abstract
The research of interval Shapley value for interval-valued cooperative games often assumes that there are some restrictions on characteristic function of this class of games,such as superadditive,convex and size monotonic.To expand the scope of the research,this paper investigates the interval-valued cooperative games without these restrictions.Firstly,we point out several shortcomings of the generalized Hukuhara difference and propose the so-called extended generalized Hukuhara difference.Then,based on extended generalized Hukuhara difference,the generalized interval Shapley value for interval-valued cooperative games is introduced.We characterize the generalized interval Shapley value using the axioms of interval efficiency,interval symmetry,interval dummy player and interval additivity.Meanwhile,we prove the existence and uniqueness of the generalized interval Shapley value and discuss some properties of this value.The study shows that an arbitrary interval-valued cooperative game has a unique generalized interval Shapley value.Finally,a numerical example is given to illustrate the feasibility and practicability of the generalized interval Shapley value.关键词
合作对策/区间数/区间Shapley值/广义H-差Key words
cooperative games/interval number/interval Shapley value/generalized Hukuhara difference分类
数理科学引用本文复制引用
邹正兴,张强..区间值合作对策的广义区间Shapley值[J].运筹与管理,2017,26(10):1-9,9.基金项目
国家自然科学基金资助项目(71771025,71371030,71401003,71561022) （71771025,71371030,71401003,71561022）
内蒙古自然科学基金(2017MS0715) （2017MS0715）
