Fuzzy quantic nuclei and conuclei with applications to fuzzy semi-quantales and (L, M)-quasi-fuzzy topologies

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.