基于软集的无标记信息代数模型与算法  

Domain-Free Information Algebraic Model and Algorithm Based on Soft Set

作　　者：许格妮[1,2] 李永明[1] 管雪冲[3] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]西安财经学院统计学院,陕西西安710100 [3]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《软件学报》2015年第5期1037-1047,共11页Journal of Software

基　　金：国家自然科学基金(11271237;61228305;11201278);陕西省自然科学基金(2014JQ9372)

摘　　要：在给定的一个初始论域U和参数集E上的全体软集中引入扩展运算与转移运算,研究了它们的性质.在此基础上引入商软集的概念,并在全体商软集中引入联合运算与聚焦运算,得到其构成一个无标记的信息代数,并且若参数集E有限,这个信息代数还是一个无标记的紧信息代数.最后,给出运用无标记信息代数的模型解决软集中不确定问题的决策算法与实例,并与Cagman等人提出的uni-int决策算法做了比较说明.Firstly, the operations of extension and transition in soft set over the universe U and the parameter E are proposed and some related properties are derived. Secondly, it is proved that the quotient soft set with the operations of combination and focusing is a domain-free information algebra. Moreover, the algebra is also compact if the set of all possible parameters is finite. Finally, an algorithm of decision making in term of the model of domain-free information algebra is presented and a corresponding example is provided to show that this model can be successfully applied to many problems. A comparison between the proposed algorithm and Cagman＇s uni-int decision making is illustrated in the end.

关 键 词：软集 扩展 转移 商软集 无标记信息代数 紧信息代数 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]