Solutions to Open Problems on Fuzzy Filters of BL-algebras
W Wei, AB Saeid - International Journal of Computational Intelligence …, 2015 - Springer
W Wei, AB Saeid
International Journal of Computational Intelligence Systems, 2015•SpringerThis paper focuses on the investigation of fuzzy filters of BL-algebras, an important and
popular generic logical algebra. By studying the equivalent conditions of fuzzy fantastic filter
and fuzzy normal filter of BL-algebras, the relation between these two filters are revealed.
Two open problems of BL-algebras, ie,“Under what suitable condition a normal filter
becomes a fantastic filter?” and “Under what suitable condition extension property for normal
filter holds?(Extension property for a normal filter)”, are solved accordingly.
popular generic logical algebra. By studying the equivalent conditions of fuzzy fantastic filter
and fuzzy normal filter of BL-algebras, the relation between these two filters are revealed.
Two open problems of BL-algebras, ie,“Under what suitable condition a normal filter
becomes a fantastic filter?” and “Under what suitable condition extension property for normal
filter holds?(Extension property for a normal filter)”, are solved accordingly.
Abstract
This paper focuses on the investigation of fuzzy filters of BL-algebras, an important and popular generic logical algebra. By studying the equivalent conditions of fuzzy fantastic filter and fuzzy normal filter of BL-algebras, the relation between these two filters are revealed. Two open problems of BL-algebras, i.e.,“Under what suitable condition a normal filter becomes a fantastic filter?” and “Under what suitable condition extension property for normal filter holds? (Extension property for a normal filter)”, are solved accordingly.
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