On regular filters and well filters of pseudo-BCI algebras
- Authors
- Zhang, Xiaohong; Park, Choonkil
- Issue Date
- Jul-2018
- Publisher
- Institute of Electrical and Electronics Engineers Inc.
- Keywords
- Non-classical logic; pseudo-BCI algebra; regular filter; well filter; anti-grouped filter; p-filter
- Citation
- ICNC-FSKD 2017 - 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery, pp.1152 - 1157
- Indexed
- SCOPUS
- Journal Title
- ICNC-FSKD 2017 - 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery
- Start Page
- 1152
- End Page
- 1157
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/149781
- DOI
- 10.1109/FSKD.2017.8392926
- Abstract
- Pseudo-BCI algebra is a kind of non-classical logic algebra; it is a generalization of pseudo-BCK algebra which is closely related to non-commutative fuzzy logic algebras. In this paper, a new notion of regular filter of pseudo-BCI algebra is proposed, and a characteristic property is given. Moreover, the relationships among regular filters and other filters of pseudo-BCI algebras are presented, and the following important propositions are proved: (1) the notions of well filter and normal filter in pseudo-BCI algebras are coincide; (2) a filter of pseudo-BCI algebra is p-filter iff (that is, if and only if) it is well anti-grouped filter (or normal anti-grouped filter); (3) a filter of pseudo-BCI algebra is regular iff it is closed anti-grouped filter; (4) a filter of pseudo-BCI algebra is an associative filer (or pseudo-a filter) if and only if it is regular T-type filter (or regular pseudo q-filter). Finally, a counterexample is given to show that a regular p-filter (or well regular filter) of pseudo-BCI algebra may be not associative filter (or pseudo-a filter).
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