λ型传递矩阵与多因素模糊决策  

λ-form transitivity matrices and multifactor fuzzy decision making

作　　者：刘文斌[1] 谷云东[2] 李洪兴[2] 

机构地区：[1]中国海洋大学数学系,山东青岛266071 [2]北京师范大学数学系,北京100875

出　　处：《高校应用数学学报（A辑）》2003年第1期70-76,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(69974006)

摘　　要：基于已知常用的模糊矩阵传递性概念定义了λ型传递.给出它的几个等价条件.研究它的图论特征,指出λ型传递矩阵的圈都过强对边二元圈.随后证明了与全传递模糊矩阵的等价性.进一步研究与截矩阵的性质一致问题,证明了λ型传递满足一致性.最后给出λ型传递在模糊排序中的应用,表明它是一种新的实用的多因素模糊决策的数学模型.A kind of transitive matrices is defined based on several concepts used commonly for transitivity of fuzzy matrices,and called λ\|form transitivity matrices.Its equivalent conditions and the characters of graph theory are researched,especially it is proved that it is equivalent with fully transitive matrices.Besides,the property consistency between λ transitive matrices and their cut matrices are studied,and a new example of the consistent property is obtained.At last,the usage of λ\|form transitive matrix as a model of ordering fuzzy quantities is discussed.It is revealed that λ\|form transitive matrix is a new type of useful mathematical model for multifactor decision making.

关 键 词：模糊矩阵 传递性 全传递矩阵 模糊排序 模糊决策 

分 类 号：O159[理学—数学]