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State BL-algebras

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Abstract

The concept of a state MV-algebra was firstly introduced by Flaminio and Montagna (An algebraic approach to states on MV-algebras. In: Novák V (ed) Fuzzy logic 2, proceedings of the 5th EUSFLAT conference, September 11–14, Ostrava, vol II, pp 201–206, 2007; Int J Approx Reason 50:138–152, 2009) as an MV-algebra with internal state as a unary operation. Di Nola and Dvurečenskij (Ann Pure Appl Logic 161:161–173, 2009a; Math Slovaca 59:517–534, 2009b) gave a stronger version of a state MV-algebra. In the present paper, we introduce the notion of a state BL-algebra, or more precisely, a BL-algebra with internal state. We present different types of state BL-algebras, like strong state BL-algebras and state-morphism BL-algebras, and we study some classes of state BL-algebras. In addition, we give a sample of important examples of state BL-algebras and present some open problems.

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Acknowledgment

L. C. Ciungu thanks SAIA for the fellowship in Slovakia, Summer 2009, A. Dvurečenskij and A. Hyčko are thankful for the support by Center of Excellence SAS, Quantum Technologies, ERDF OP R&D Project CE QUTE ITMS 26240120009 and meta-QUTE ITMS 26240120022, the grants VEGA Nos. 2/0032/09, 2/7142/27 SAV and by the Slovak Research and Development Agency under the contract No. APVV-0071-06, Bratislava.

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Authors and Affiliations

  1. Polytechnical University of Bucharest, Splaiul Independenţei 113, Bucharest, Romania

    Lavinia Corina Ciungu

  2. State University of New York, Buffalo, 244 Mathematics Building, Buffalo, NY, 14260-2900, USA

    Lavinia Corina Ciungu

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij & Marek Hyčko

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  1. Lavinia Corina Ciungu
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  2. Anatolij Dvurečenskij
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  3. Marek Hyčko
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Correspondence to Anatolij Dvurečenskij.

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Ciungu, L.C., Dvurečenskij, A. & Hyčko, M. State BL-algebras. Soft Comput 15, 619–634 (2010). https://doi.org/10.1007/s00500-010-0571-5

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