Łukasiewicz fuzzy filters in hoops

By applying the concept of the Łukasiewicz fuzzy set to the filter in hoops, the Łukasiewicz fuzzy filter is introducedand its properties are investigated. The relationship between fuzzy filter and Łukasiewicz fuzzy filter is discussed.Conditions for the Łukasiewicz fuzzy set to be a Łukasiewicz fuzzy filter are provided, and characterizations ofŁukasiewicz fuzzy filter are displayed. The conditions under which the three subsets, ۲-set, q-set, and O-set, willbe filter are explored

Keywords:

Łukasiewicz fuzzy set , Łukasiewicz fuzzy filter , ۲-set , q-set , O-set.