Fuzzy Filters of Pre-ordered Residuated Systems
Young Bae Jun
1
(
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, 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.
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