Fuzzy Filters of Pre-ordered Residuated Systems
Young Bae Jun
1
(Department of Mathematics EducationGyeongsang National UniversityChinju 660-701, Korea.)
Keywords: Residuated relational system, Pre-ordered residuated system, Filter, $\in_{t}$-set, (Extended) $q_{t}$-set, Positive set.,
Abstract :
Using the concept of fuzzy points, the notion of fuzzy filters in pre-ordered residuated systems is introduced, and their relevant properties are investigated and analyzed. Characterization of fuzzy filters are displayed. Fuzzy filters are formed using filters. The concepts of positive set, $\in_{t}$-set, (extended) $q_{t}$-set are defined and the conditions under which they become filters are explored. The concept of fuzzy filter with thresholds is introduced and related properties are investigated.
[1] Bonzio S, Chajda I. Residuated relational systems. Asian-European Journal of Mathematics. 2018; 11(02): 1850024. DOI: https://doi.org/10.1142/S1793557118500249
[2] Pao-Ming P, Ying-Ming L. Fuzzy topology I, Neighborhood structure of a fuzzy pointand Moore- Smith convergence. Journal of Mathematical Analysis and Applications. 1980; 76(2): 571-599. DOI: https://doi.org/10.1016/0022-247X(80)90048-7
[3] Romano DA. Filters in residuated relational system ordered under quasi-order. Bul- letin of the International Mathematical Virtual Institute. 2020; 10(3): 529-534. DOI: http://doi.org/10.7251/BIMVI2003529R
[4] Romano DA. Comparative filters in quasi-ordered residuated system. Bulletin of the International Math- ematical Virtual Institute. 2021; 11(1): 177-184. DOI: http://doi.org/10.7251/BIMVI2101177R
[5] Romano DA. Implicative filters in quasi-ordered residuated systems. Proyecciones Journal of Mathemat- ics. 2021; 40(2): 417-424. DOI: http://dx.doi.org/10.22199/issn.0717-6279-2021-02-0025
[6] Romano DA. Weak implicative filters in quasi-ordered residuated systems. Proyecciones Journal of Math- ematics. 2021; 40(3): 797-804. DOI: http://dx.doi.org/10.22199/issn.0717-6279-4332
[7] Romano DA. Shift filter of quasi-ordered residuated systems. Communications in Advanced Mathematical Sciences. 2022; 5(3): 124-130. DOI: http://doi.org/10.33434/cams.1089222
