The aim of this paper is to introduce and study the notions of M-fuzzy quantic nuclei and
conuclei on quantales. Firstly, the concept of an M-fuzzy quantic nuclei is introduced
and some of its properties are discussed. Secondly, the concept of an M-fuzzy quantic
conuclei is introduced. As an application of M-fuzzy quantic conuclei on quantales, a
characterization of an (L, M)-quasi-fuzzy interior operator on a non-empty set X is given
and the relationship between it and an (L, M)-quasi-fuzzy topology is discussed. Finally,
the concept of an M-fuzzy left (resp., right) ideal conucleus is introduced and the
relationship with the concept of M-fuzzy left (resp., right) ideal is introduced.