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Some types of filters in residuated lattices

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Abstract

In this paper, inspired by some types of \(BL\)-algebra filters (deductive systems) introduced in Haveshki et al. (Soft Comput 10:657–664, 2006), Kondo and Dudek (Soft Comput 12:419–423, 2008) and Turunen (Arch Math Log 40:467–473, 2001), we defined residuated lattice versions of them and study them in connection with Van Gasse et al. (Inf Sci 180(16):3006–3020, 2010), Lianzhen and Kaitai (Inf Sci 177:5725–5738, 2007), Zhu and Xu (Inf Sci 180:3614–3632, 2010). Also we consider some relations between these filters and quotient residuated lattice that are constructed via these filters.

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Acknowledgments

The authors wish to express their appreciation for several excellent suggestions for improvements made by the referees.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Craiova, 13, Al.I. Cuza st., 200585 , Craiova, Romania

    Dumitru Buşneag & Dana Piciu

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  1. Dumitru Buşneag
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  2. Dana Piciu
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Correspondence to Dumitru Buşneag.

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Communicated by A. Ciabattoni.

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Buşneag, D., Piciu, D. Some types of filters in residuated lattices. Soft Comput 18, 825–837 (2014). https://doi.org/10.1007/s00500-013-1184-6

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