Relations between W_d-fuzzy implication algebras and other logical algebras

In this paper, we continue the study W_d-fuzzy implication algebras which are subalgebras of fuzzy implication algebras. Properties and axiomatic systems for W_d-fuzzy implication algebras are presented, then a few new results on W_d-fuzzy implication algebras have been added. We showed that there are relations between W_d-fuzzy implication algebras and some of other fuzzy logical algebras such as FI-algebras, RFI-algebras, CFI-algebras, HFI-algebras. In particular, the relations between W_d-fuzzy implication algebras and L-algebras are investigated, and we prove that every W_d-fuzzy implication algebras is a proper subclass of L-algebras. Finally, we introduce the notions of GW_d-FI algebras, whose some properties of it are investigated. The relations between distributive GW_d-FI-algebras, Hilbert algebras, BE-algebras and W-eo algebras have been obtained.