Fuzzy multiply positive implicative hyper BCK-ideals of hyper BCK-algebras (Q1774741)

In a hyper BCK-algebra \((H,\circ,0)\) the symbol \(x\circ y^n\) denotes \((\dots((x\circ y)\circ y)\circ\ldots)\circ y\), where \(y\) is used \(n\) times. A nonempty subset \(I\) of \(H\) is a multiply positive implicative hyper BCK-ideal if \(0\in I\) and for any \(x,y,z\in H\) such that \((x\circ y)\circ z^n\ll I\) and \(y\circ z^m\ll I\) there exists a natural number \(k=k(x,y,z)\) for which \(x\circ z^k\ll I\). Fuzzification of ideals defined in this way is presented. A part of the results are an extension of results obtained by \textit{W. A. Dudek, Y. B. Jun}, and \textit{Z. Stojaković} [Fuzzy Sets Syst. 123, 251--258 (2001; Zbl 1018.06016)] to the case of hyper BCK-algebras.