The Research On The Application Of Soft Set Theory In The Fuzzy Logical Algebras

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.