In this paper, we introduce a novel fuzzy structure named "fuzzy primal". We
study the essential properties and discuss basic operations on it. A fuzzy
operator (.)β on the family of all fuzzy sets is introduced here by
applying the q-neighborhood structure to a primal fuzzy topological space along
with the Lukasiewicz disjunction. We explore the main characterizations of
(.)β. Then, we define another fuzzy operator, symbolized by
Clβ, with the utilization of (.)β. These fuzzy operators
are studied in order to deduce a new fuzzy topology from the original one. Such
a new fuzzy topology is called primal fuzzy topology. The fundamental
structure, particularly a fuzzy base that generates primal fuzzy topologies, as
well as many relationships between different fuzzy primals and fuzzy
topologies, are also analyzed. Lastly, the concept of compatibility between
fuzzy primals and fuzzy topologies is introduced, and some equivalent
conditions related to this are examined. It is shown that if a fuzzy primal is
compatible with a fuzzy topology, then the fuzzy base that generates the primal
fuzzy topology is itself a fuzzy topology