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http://dx.doi.org/10.11568/kjm.2019.27.4.1119

ON GENERALIZED f-DERIVATIONS OF LATTICE IMPLICATION ALGEBRAS  

Kim, Kyung Ho (Department of Mathematics Korea National University of Transportation)
Publication Information
Korean Journal of Mathematics / v.27, no.4, 2019 , pp. 1119-1131 More about this Journal
Abstract
In this paper, we introduce the notion of generalized f-derivation of lattice implication algebra and investigate some related properties. Also, we prove that if D is a generalized f-derivation associated with an f-derivation d of L, then D(x → y) = f(x) → D(y) for all x, y ∈ L.
Keywords
Lattice implication algebra; generalized f-derivation; isotone; $Fix_D(L)$; KerD;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 J. A. Goguen, The logic of inexact concepts, Synthese 19 (1969), 325-373.   DOI
2 S. D. Lee and K. H. Kim, On derivations of lattice implication algebras, Ars Combinatoria 108 (2013), 279-288.
3 J. Liu and Y. Xu, On certain filters in lattice implicationalgebras, Chinese Quarterly J. Math. 11 (4) (1996), 106-111.
4 J. Liu and Y. Xu, On the property (P) of lattice implicationalgebras, J. Lanzhou Univ. 32 (1996), 344-348.
5 J. Liu and Y. Xu, Filters and structure of lattice implicationalgebras, Chinese Science Bulletin 42 (18) (1997), 1517-1520.   DOI
6 C. Prabpayak and U. Leerawat, On derivations of BCC-algebras, Kasetsart J. 43 (2009), 398-401.
7 Z. M. Song, Study on the theoretical foundation of uncertainty information processing based on lattice implication algebras and method of uncertainty reasoning, Ph. D. Thesis, Southwest Jiaotong University, China (1998) (in Chinese).
8 Y. Xu, Lattice implication algebras, J. Southwest Jiaotong Univ. 1 (1993), 20-27.
9 Y. Xu and K. Y. Qin, Lattice H implication algebras and lattice implicationalgebra classes, J. Hebei Mining and Civil Engineering Institute 3 (1992), 139-143.
10 Y. Xu and K. Y. Qin, On filters of lattice implicationalgebras, J. Fuzzy Math. 1 (2) (1993), 251-260.
11 Y. H. Yon and K. H. Kim, On f-derivations of lattice implication algebras, Ars Combinatoria, 110 (2013), 205-215.
12 L. Bolc and P. Borowik, Many-Valued Logic, Springer, Berlin, 1994.
13 Yilmaz Ceven and Mehmet Ali Ozturk, On f-derivations of lattice, Bull. Korean Math. Soc 45 (2008), 701-707.   DOI
14 Alev Firat, On f-derivations of BCC-algebras, Ars Combinatoria, XCVIIA (2010), 377-382.