University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065416620191201Weak hyper semi-quantales and weak hypervalued topological spaces4351501810.22111/ijfs.2019.5018ENK.El-SaadyDepartment of Mathematics, Faculty of Science, South Valley University, Qena, 83523, EGYPTJournal Article20191118The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories.<br /> Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued topology (or many-valued topology). Some properties of weak hyper semi-quantales and weak hypervalued-topologies will be studied. An adjunction between the category of weak hyper semi-quantales and the category of weak hypervalued quasi-topological spaces will be established.https://ijfs.usb.ac.ir/article_5018_a0662cf56a119fd62a0558f2b2443106.pdf