Busneag, D., Piciu, D. (2016). Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices. Iranian Journal of Fuzzy Systems, 13(1), 145-160. doi: 10.22111/ijfs.2016.2294

D. Busneag; D. Piciu. "Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices". Iranian Journal of Fuzzy Systems, 13, 1, 2016, 145-160. doi: 10.22111/ijfs.2016.2294

Busneag, D., Piciu, D. (2016). 'Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices', Iranian Journal of Fuzzy Systems, 13(1), pp. 145-160. doi: 10.22111/ijfs.2016.2294

Busneag, D., Piciu, D. Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices. Iranian Journal of Fuzzy Systems, 2016; 13(1): 145-160. doi: 10.22111/ijfs.2016.2294

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

^{1}Department of Mathematics, Faculty of Mathematics and Natural Sci- ences, University of Craiova, Craiova, Romania

^{2}Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Craiova, Craiova, Romania

Abstract

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.

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