TY  - JOUR
TT  - Some Results on Stabilizers in Residuated Lattices
AU  - Haveshki, Masoud
PY  - 2014
DA  - November
JF  - Cankaya University Journal of Science and Engineering
JO  - CUJSE
PB  - Cankaya University
WT  - DergiPark
SN  - 2564-7954
VL  - 11
IS  - 2
KW  - Residuated lattices
KW  - stabilizer
KW  - implicative filter
KW  - positive implicative filter
KW  - fantastic filter
KW  - obstinate filter.
N2  - Borumand and Mohtashamnia in [1] introduced the notion of the (right and left) stabilizer inresiduated lattices and proved some theorems which determine the relationship between this notion and sometypes of filters in residuated lattices. In this paper, we show that a part of Theorem 3.10 [1] is not correct.Borumand and Mohtashamnia proved Theorem 4.2 [1] with some conditions. We prove this theorem withoutany condition. Also, we prove Theorem 3.8 and part (4) of Proposition 3.3 in [1] more generally and finallyobtain some new and useful theorems on stabilizers in residuated lattices.
CR  - [1] A. Borumand Saeid, N. Mohtashamnia, Stabilizer in residuated lattices, University Politehnica of Bucharest, Scientific Bulletin Series A - Applied Mathematics and Physics, 74(2), (2012), 65–74.
CR  - [2] P. Cintula, P. H ´ajek, C. Noguera, Handbook of Mathematical Fuzzy Logics, College Publications, (2011).
CR  - [3] P. H ´ajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, (1998).
CR  - [4] C. Muresan, Dense Elements and Classes of Residuated Lattices, Bull. Math. Soc. Sci. Math. Roumanie Tome, 53(101)(1), (2010), 11–24.
CR  - [5] D. Piciu, Algebras of Fuzzy Logic, Ed. Universitaria Craiova, (2007).
CR  - [6] E. Turunen, Mathematics Behind Fuzzy Logic, Physica-Verlag, (1999).
CR  - [7] Y. Zhu, Y. Xu, On filter theory of residuated lattices, Information Sciences, 180, (2010), 3614–3632.
UR  - https://dergipark.org.tr/en/pub/cankujse/issue//368685
L1  - https://dergipark.org.tr/en/download/article-file/386839
ER  -