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Extended filters in bounded commutative Rl-monoids

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Abstract

The notion of extended filter of a filter associated to a subset of Rl-monoids is defined and related properties are investigated. Rachunek and Salounova proved that positive implicative filters and Boolean filters in Rl-monoids coincide with a condition in Rachunek and Salounova (Acta Univ Palacki Olomuc Fac rer nat Math 48(1):93–107, 2009). In this paper, we prove that positive implicative filters and Boolean filters coincide without any condition and get some results on various types of filters.

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Acknowledgments

The author is very indebted to the referees for valuable suggestions that improved the readability of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Hormozgan University, P.O. Box 3995, Bandarabbas, Iran

    Masoud Haveshki & Mahboobeh Mohamadhasani

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  1. Masoud Haveshki
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  2. Mahboobeh Mohamadhasani
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Correspondence to Masoud Haveshki.

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Haveshki, M., Mohamadhasani, M. Extended filters in bounded commutative Rl-monoids . Soft Comput 16, 2165–2173 (2012). https://doi.org/10.1007/s00500-012-0884-7

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