【作者】 刘婷；

【导师】 刘练珍；

【作者基本信息】 江南大学 ， 应用数学， 2010， 硕士

【摘要】 软集合理论是由Molodtsov在1999年提出的,它是一种新的处理模糊和不确定性模型的数学工具.由于软集合中的参数可以取任意形式,使得该理论在数学,经济学,工程学和物理学等领域中都得到了广泛应用.本文将软集合理论运用到模糊逻辑代数中.研究并讨论了软BCI-代数的软关联理想、软正定关联理想和软可换理想,软BL-代数的软滤子、软蕴涵滤子、软正蕴涵滤子和软奇异滤子,并对它们的性质进行了研究.得到一系列有意义的结果,丰富了软集合理论的代数结构.具体内容如下:(1)给出软BCI-代数的软关联理想、软正定关联理想和软可换理想的概念.讨论了软理想、软关联理想、软正定关联理想和软可换理想之间的关系,并对两个软关联理想(软正定关联理想,软可换理想)的扩展交、限制交、限制并、限制差分的运算性质和软相等关系进行了研究.得到两个软关联理想(软正定关联理想,软可换理想)的扩展交,限制交依然是一个软关联理想(软正定关联理想,软可换理想),同时,给出实例说明两个软关联理想(软正定关联理想,软可换理想)的限制并、限制差分不是软关联理想(软正定关联理想,软可换理想).(2)在软BL-代数上提出了软滤子、软蕴涵滤子、软正蕴涵滤子和软奇异滤子的概念,讨论软滤子、软蕴涵滤子、软正蕴涵滤子和软奇异滤子之间的关系,并对两个软滤子(软蕴涵滤子、软正蕴涵滤子、软奇异滤子)的软相等关系和偏序关系进行了研究.更多还原

【Abstract】 The soft set theory was introduced by D Molodtsov in 1999. It is a new mathematical tool for dealing with vagueness and uncertainty model. As the parameters of soft sets can take any form, the theory has been widely used in mathematics, economics, engineering, physics and other fields.In this paper, the soft set theory is applied to fuzzy logical algebras. Soft implicative ideals, soft positive implicative ideals, soft commutative ideals of BCI-algebras, soft filters, soft implicative filters, soft positive implicative filters, soft fantastic filters of BL-algebras are studied. Meanwhile, some fundamental properties of them are discussed. The results obtained in this paper, enrich the algebraic structure of the soft set theory. We list the main results as follows:(1) The definitions of soft implicative ideals, soft positive implicative ideals, soft commutative ideals of BCI-algebras are introduced. Then, the relations among the soft ideals, the soft implicative ideals, the soft positive implicative ideals and the soft commutative ideals are discussed. Furthermore, the extended intersection operation, the restricted intersection operation, the restricted union operation, the restricted difference operation and soft equality relation of two soft implicative ideals (soft positive implicative ideals, soft commutative ideals) are studied. And we have got that the extended intersection operation (the restricted intersection operation) of two soft implicative ideals (soft positive implicative ideals, soft commutative ideals) is still a soft implicative ideal (soft positive implicative ideal, soft commutative ideal). Moreover, we give some examples to illustrate that the restricted union operation, the restricted difference operation of two soft implicative ideals (soft positive implicative ideals, soft commutative ideals) may not be a soft implicative ideal (soft positive implicative ideal, soft commutative ideal).(2) The notions of soft filters, soft implicative filters, soft positive implicative filters and soft fantastic filters in soft BL-algebras are proposed. Then, the relations among the soft filters, the soft implicative filters, the soft positive implicative filters and the soft fantastic filters are investigated. Both the soft equality relation and the partial ordering relation of two soft implicative filters (soft positive implicative filters, soft fantastic filters) are studied.更多还原