Abstract
Lattice implication algebra is a logical algebraic system which is constructed by combining lattice with implication algebra. In this paper, we focus on the extension of LI-ideal of lattice implication algebras, i.e., weak LI-ideals (briefly, WLI-ideals) and maximal weak LI-ideals. The properties of weak LI-ideals are studied and several characterizations of weak LI-ideals are given. Finally, we study the relationships among WLI-ideals, LI-ideals and Lattice ideals.
This project was supported by the National Science Foundation of P.R. China under Grant No. 60474022, and the specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20060613007.
Brief introduction of author: Lai Jiajun, male, study the direction: Logic algebra.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Borns, D.W., Mack, J.M.: An algebraic Introduction on Mathematical logic. Springer, Berlin (1975)
Bolc, L., Borowik, P.: Many-valued Logics. Springer, Heidelberg (1992)
Ben-Eliyahu, R., Dechter, R.: Default reasoning using classical logic. Artificial Intelligence 84, 113–150 (1996)
Goguen, J.A.: The logic of inexact concepts. Synthese 19, 325–373 (1969)
Pavelka, J.: On fuzzy logic I, II, III. Zeitschr. F. Math. Logic and Grundlagen der Math. 25, 45-52, 119-134, 447-464 (1979)
Novak, V.: First-order fuzzy logic. Studia Logica 46(1), 87–109 (1982)
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)
Liu, J., Xu, Y.: On filters and structures of lattice implication algebras (in Chinese). Chinese Science Bulletin 42(10), 1049–1052 (1997)
Xu, Y., et al.: L-valued propositional logic. Information Sci. 114, 205–235 (1999)
Xu, Y., et al.: Fuzzy reasoning based on the extension principle. Int. J. Intelligent System 16(4), 469–495 (2001)
Xu, Y., et al.: -Resolution principle based on first-order lattice-valued logic LF(X). Information Sci. 132, 221–239 (2001)
Jun, Y.B., Roh, E.H., Xu, Y.: LI-ideals in lattice implication algebras. Bull. Korean Math. Soc. 35, 13–24 (1998)
Jun, Y.B.: On LI-ideals and prime LI-ideals of lattice implication algebras. Bull. Korean Math. Soc. 36(2), 369–380 (1999)
Jun, Y.B., et al.: Intuitionistic fuzzy LI-ideals in lattice implication algebras. Sci. Math. 3(2), 185–192 (2000)
Jun, Y.B., Xu, Y.: Fuzzy LI-ideals in lattice implication algebras. J. Fuzzy Math. 7(4), 997–1003 (1999)
Jun, Y.B., Xu, Y., Qin, K.Y.: Normal fuzzy LI-ideals in lattice implication algebras. J. Fuzzy Math. 7(4), 1045–1052 (1999)
Liu, Y.L., et al.: ILI-ideals and prime LI-ideals in lattice implication algebras. Int. J. Information Sci. 155, 157–175 (2003)
Huang, T.M., Xu, Y., et al.: Application and Introductions of Lattice and Order. Southwest Jiaotong University Press, Chengdu (1998)
Jun, Y.B.: On LI-ideals and prime LI-ideals of lattice implication algebras. Bull. Korean Math. Soc. 36(2), 369–380 (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jiajun, L., Yang, X., Ma, J. (2007). On Extension of LI-Ideal in Lattice Implication Algebra . In: Castillo, O., Melin, P., Ross, O.M., Sepúlveda Cruz, R., Pedrycz, W., Kacprzyk, J. (eds) Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. Advances in Soft Computing, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72434-6_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-72434-6_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72433-9
Online ISBN: 978-3-540-72434-6
eBook Packages: EngineeringEngineering (R0)