Characterization of different classes of intuitionistic fuzzy filters of lattice wajsberg algebra

Abstract

The present research deals with the new classes of intuitionistic fuzzy filters of Lattice Wajsberg Algebra. Their characterizations, various properties and interrelations have been presented. Intuitionistic fuzzy filter and intuitionistic fuzzy lattice filter have been defined and the relations between them have been defined. Some properties of intuitionistic fuzzy filter are proved. The intersection of two intuitionistic fuzzy filters to be an intuitionistic fuzzy filter is derived. Intuitionistic fuzzy Boolean filter have been defined and the intersection of intuitionistic fuzzy Boolean filters to be intuitionistic fuzzy Boolean filter is proved. Intuitionistic fuzzy implicative filter is defined and the equivalent condition for an intuitionistic fuzzy set to be intuitionistic fuzzy implicative filter is obtained. Further, the relations between intuitionistic fuzzy filter and intuitionistic fuzzy implicative filter have been defined. Necessary and sufficient condition for an intuitionistic fuzzy set to be intuitionistic fuzzy implicative filter is obtained. Intuitionistic fuzzy prime filter is also defined and its properties are obtained. Intuitionistic fuzzy regular filter, intuitionistic fuzzy ultra filter and intuitionistic fuzzy obstinate filter, intuitionistic fuzzy normal filter are defined and their interrelations are presented. Counterexamples are given to prove that the reverse implications are not possible in some cases. Moreover, equivalent conditions and some properties for these filters are also obtained. Similarly, intuitionistic fuzzy n-fold Boolean filter and intuitionistic n-fold implicative filter are defined and their interrelations are seen. The intersection of intuitionistic fuzzy n-fold Boolean filters to be intuitionistic fuzzy n-fold Boolean filter is presented newline