Abstract
In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak filters and right weak filters of a weak PQW-algebra and study related properties of them. We also discuss the relation between normal filters and filter congruences on a weak PQW-algebra. Finally, we characterize the relationship between weak PQW-algebras and some bounded residuated quasi-ordered monoids with supplementary conditions.
Funder
National Natural Science Foundation of China
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference24 articles.
1. A new proof of the completeness of Lukasiewicz axioms;Chang;Trans. Am. Soc.,1959
2. Metamathematics of Fuzzy Logic;Hajek,1998
3. Monoidal t-norm based logictowards a logic for left-continuous t-norms
4. An introduction to the theory of BCK-algebras;Iséki;Math. Jpn.,1978
5. On the BCI-G part of BCI-algebras;Jun;Math. Jpn.,1993