The subsets T, I, F are not necessarily intervals, but may be any real subsets: discrete or continuous; single-element, finite, or (either countably or uncountably) infinite; union or intersection of various subsets; etc.

In this paper, Florentin Smarandache, reputed professor at University of New Mexico, presents a new branch of philosophy, called neutrosphy, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Florin Smarandache is not only a high level scientist, he is also a propensity and complete artist who wanted to express and to share his cognition, thoughts, ideas in a moment and in a place when and where, was not possible, it was necessary to find the way to communicate somehow: so, it was born “the paradoxism”.

N-Norm and N-conorm are extended in Neutrosophic Logic/Set.

In this paper we define the MBJw – filters of Lattice wajsberg algebras and proved the properties ofMBJw – filters. We derive some relation between fuzzy ideals, interval valued fuzzy ideals to neutrosophic ideals. Further we prove that cut sets of MBJ – sets formed MBJ w – filter. Finally define the MBJ w– lattice filters and proved every MBJw – filter is a MBJw – lattice filter and converse is not true.