On Lukasiewicz Fuzzy Implicative and Positive Implicative Filter of Hoops

This work presents the ideas of Lukasiewicz fuzzy implicative filters and Lukasiewicz fuzzy positive implicative filters within the context of hoops.We provide a detailed characterization of the conditions under which a Lukasiewicz fuzzy set can be regarded as a Lukasiewicz fuzzy implicative filter and Lukasiewicz fuzzy positive implicative filter.Additionally, we examine the relationship between these filter types with Lukasiewicz fuzzy filter.Furthermore, the relationship between Lukasiewicz fuzzy implicative filter and Lukasiewicz fuzzy positive implicative filter is analyzed.