Benelbar, KhawlaSupervisor: Milles, Soheyb2022-07-252022-07-252022-06-10http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/30961,Ty AbR T wm ,TkbJ Abstract In this work, we generalize the notion of principal ideal (resp. filter) on a lattice to the setting of fuzzy sets and investigate their various characterizations and properties. More specifically, we show that any principal fuzzy ideal (resp. filter) coincides with a fuzzy down-set (resp. up-set) generated by a fuzzy singleton. Afterwards, for a given fuzzy set, we introduce two fuzzy sets : its fuzzy down-set and up-set, and we investigaensting properties. Key words : Lattice, fuzzy set, Principal fuzzThesis