On fuzzy BCC-ideals over a t-norm (Q2708494)

The authors extend the concept of fuzzy BCC-ideals to that of \(T\)-fuzzy BCC-ideals and investigate their properties. While fuzzy BCC-ideals are defined by using the min-operator on \([0,1]\), \(T\)-fuzzy BCC-ideals are defined by using a t-norm \(T\), which is an extension of the min-operator.NEWLINENEWLINENEWLINEThe following results are proved:NEWLINENEWLINENEWLINE1. Every \(T\)-fuzzy BCK-ideal is a \(T\)-fuzzy BCC-ideal;NEWLINENEWLINENEWLINE2. For \(T\)-fuzzy BCC-ideals \(\mu\), \(\nu\), the \(T\)-product \([\mu\cdot\nu]_T\) of \(\mu\) and \(\nu\) is also a \(T\)-fuzzy BCC-ideal;NEWLINENEWLINENEWLINE3. If \(\mu_i\) is a \(T\)-fuzzy BCC-ideal of BCC-algebras \(G_i\) \((i\leq n)\), then so is the product \(\prod\mu_i\) of \(\mu_i\).NEWLINENEWLINENEWLINEEach of the above results is an extension of the following well-known ones:NEWLINENEWLINENEWLINE1. Every fuzzy BCK-ideal is a fuzzy BCC-ideal;NEWLINENEWLINENEWLINE2. For fuzzy BCC-ideals \(\mu\), \(\nu\), the product \(\mu\cdot\nu\) of \(\mu\) and \(\nu\) is also a fuzzy BCC-ideal;NEWLINENEWLINENEWLINE3. If \(\mu_i\) is a fuzzy BCC-ideal of BCC-algebras \(G_i\) \((i\leq n)\), then so is the product \(\prod \mu_i\) of \(\mu_i\).