Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices

After the research on naBL-algebras gained by non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of generalization BL-algebras, which can be obtained general functions. In this paper, we show that not every function induce an BL-algebra counterexample thus propose new concept weak BL-algebras. We prove each corresponds to BL-algebra; therefore, two mistaken results in previous paper are revised. addition, some properties satisfied discussed, relationships among non-classical logic algebras analyzed. Finally, establish theory filters quotient residuated lattice (IGRL) pseudo-general (IPGRL), characterize kinds IGRLs IPGRLs naBL-filters, (weak) BL-filters, pseudo-BL-filters.