Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices

  • سال انتشار: 1395
  • محل انتشار: مجله سیستم های فازی، دوره: 13، شماره: 1
  • کد COI اختصاصی: JR_IJFS-13-1_011
  • زبان مقاله: انگلیسی
  • تعداد مشاهده: 91
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نویسندگان

D. Busneag

Department of Mathematics, Faculty of Mathematics and Natural Sci- ences, University of Craiova, Craiova, Romania

D. Piciu

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Craiova, Craiova, Romania

چکیده

At present, the filter theory of BLtextit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{۴}, cite{۵}, cite{xi}, cite{۶}, cite{۷}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor BLtextit{-}algebras. Note that filters are also characterized byvarious types of fuzzy sets. Most of such characterizations is trivial butsome 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 inevidence 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.

کلیدواژه ها

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

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