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Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 11، دوره 13، شماره 1، اردیبهشت 2016، صفحه 145-160 اصل مقاله (379.32 K) | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2294 | ||
| نویسندگان | ||
| D. Busneag* 1؛ D. Piciu2 | ||
| 1Department of Mathematics, Faculty of Mathematics and Natural Sci- ences, University of Craiova, Craiova, Romania | ||
| 2Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Craiova, Craiova, Romania | ||
| چکیده | ||
| At present, the filter theory of $BL$textit{-}algebras has been widely studied, and some important results have been published (see for example cite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such as cite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory in the more general setting of residuated lattices is done, generalizing that for $BL$textit{-}algebras. Note that filters are also characterized by various types of fuzzy sets. Most of such characterizations is trivial but some are nontrivial, for example characterizations obtained in cite{xm}. Both situation have revealed a rich range of classes of filters: Boolean, implicative, Heyting, positive implicative, fantastic (or MV-filter), etc. In this paper we work in the general cases of residuated lattices and put in evidence new types of filters in a residuated lattice (in the spirit of cite {mvl}): semi-G-filterstextit{, }Stonean filters, divisible filters, BL-filters and regular filters. | ||
| کلیدواژه‌ها | ||
| residuated lattice؛ Boolean algebra؛ BL-algebra؛ MV-algebra؛ MTL-algebra؛ Divisible residuated lattice؛ Regular residuated lattice؛ Deductive system؛ Filter؛ Boolean filter؛ MTL-filter؛ Divisible filter؛ BL-filter؛ MV-filter؛ Semi-G-filter؛ Stonean filter؛ Regular filter | ||
| مراجع | ||
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