基于关系代数的软集合理论研究与应用

Extension and Application of Soft Set Theory Based on Relational Algebra

基于关系代数理论中的部分思想,定义了软集合理论中的差运算、选择运算和投影运算.探讨了关系代数和软集合的关系,运用关系代数的选择、投影、并、差等运算实现了软集合参数约简算法,并用SQL语言实现了算法.最后将算法运用到房屋置业选择问题中进行验证.结果表明,软集合方法能以一种更简单直接的形式为决策问题提供有效的参考依据.

This paper defines difference operation of two soft sets,selection operation and projection operation of a soft set theory,and gives a proof that any soft set over a finite domain can be represented by a two-dimensional table which is also a relation table.A detailed algorithm of parameters reduction of a soft set based on basic operation of relational algebra is provided,which is implemented by selection operation,projection operation,union operation and difference operation of relational algebra in SQL.At last,the algorithm is applied for solving the question of house selection.The result shows that soft sets can provide a direct and concise form to make decisions.