Abstract
In this paper, we introduced the notions of fuzzy lattice filter (briefly, FL-filter), and normal fuzzy filters (briefly, NF-filter) of lattice implication algebras. And we also studied the properties of FL-filters, NF-filters in lattice implication algebra. Several characteristic of FL-filters and NF-filters are given. Respectively the relation between FL-filters and NF-filters, between fuzzy filters and FL-filters are investigated. This article aims at discussing new development of fuzzy filters and its properties.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Borns, D.W., Mack, J.M.: An algebraic Introduction on Mathematical Logic. Springer, Berlin (1975)
Xu, Y.: Lattice implication algebras (in Chinese). J. Southwest Jiaotong Univ. 28(1), 20–27 (1993)
Xu, Y., et al.: Lattice-Valued Logic. Springer, Berlin (2003)
Xu, Y., Qin, K.Y.: Lattice H implication algebras and lattice implication algebra classes (in Chinese). J. Hebei Mining Civil Engineering Institute 3, 139–143 (1992)
Xu, Y., Qin, K.Y.: On filters of lattice implication algebras (in Chinese). J. Fuzzy Math. 1, 251–260 (1993)
Xu, Y., Qin, K.Y.: Fuzzy lattice implication algebras (in Chinese). J. Southwest Jiaotong Univ. 2, 2121–2127 (1995)
Liu, J., Xu, Y.: On filters and structures of lattice implication algebras (in Chinese)). Chinese Science Bulletin 42(10), 1049–1052 (1997)
Qin, K.Y., Xu, Y.: The Ultra-filter of lattice implication algebras (in Chinese). J. Southwest Jiaotong Univ. 34(1), 51–54 (1999)
Wang, X.F., Xu, Y., Song, Z.M.: Some of properties of filters in lattice implication algebras (in Chinese). J. Southwest Jiaotong Univ. 5, 536–539 (2001)
Jun, Y.B., Xu, Y., Qin, K.Y.: Positive implicative and associative filters of lattice implication algebras (in Chinese). J. Bull. Korean Math. Soc. 35(1), 53–61 (1998)
Zhao, J.B., Zhu, H.: Primary filter of residuated lattice implication algebras (in Chinese). J. Nanyang Teacher’s College 5(3), 14–16 (2006)
Chen, S.W., Xu, Y.: The normal fuzzy filter of lattice implication algebra. J. Fuzzy Math. 14(2) (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lai, Jj., Chen, Sw., Xu, Y., Qin, Ky., Chen, L. (2007). On Relationships of Filters in Lattice Implication Algebra. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_108
Download citation
DOI: https://doi.org/10.1007/978-3-540-71441-5_108
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71440-8
Online ISBN: 978-3-540-71441-5
eBook Packages: EngineeringEngineering (R0)