Fuzzy Soft Positive Implicative Hyper BCK-Ideals

In this paper, the author contributed the concepts of fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\) are introduced some related properties are considered. Relations between double-framed soft hyper BCK-ideal and double-framed soft strong hyper BCK-ideal are discussed. Additionally, the author demonstrate that the level set of fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\) are positive implicative hyper BCK ideal of types \((\ll ,\subseteq ,\subseteq)\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\), respectively. The conditions for a fuzzy soft set to be a fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\), are initiated respectively, and the circumstances for a fuzzy soft set to be a fuzzy soft weak hyper BCK-ideal are also considered.