Soft Computing

, Volume 21, Issue 19, pp 5631–5639 | Cite as

The decomposition of linearly ordered pseudo-hoops

Foundations
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Abstract

We generalize to the non-commutative case a construction of the Hájek decomposition using an equivalence relation on linear pseudo-hoops. Other two equivalence relations are used to obtain the Agliano–Montagna and the Cignoli–Esteva–Godo–Torrens decompositions. The comparability of the three decompositions follows from this construction.

Keywords

Non-commutative fuzzy logic Pseudo-hoops Ordinal sum decomposition 

Notes

Acknowledgments

The author’s participation to LATD 2012 was possible due to a travel grant and to local support from the organizers.

Compliance with ethical standards

Conflict of interest

The author declares that, apart from the above, she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Agliano P, Montagna F (2003) Varieties of BL-algebras I: general properties. J Pure Appl Algebra 181:105–129MathSciNetCrossRefMATHGoogle Scholar
  2. Busaniche M (2004) Decomposition of BL-chains. Algebra Universalis 52:519–525MathSciNetCrossRefMATHGoogle Scholar
  3. Ceterchi R (2001) Pseudo–Wajsberg algebras. Mult-Valued Log 6(1–2):67–88 (a special issue dedicated to the memory of Gr. C. Moisil)MathSciNetMATHGoogle Scholar
  4. Ceterchi R (2012) The Decomposition of linearly ordered pseudo-hoops. In: LATD 2012, 10–14 September 2012, Kanazawa, Ishikawa, JapanGoogle Scholar
  5. Ceterchi R (2014) A categorical equivalence for a class of product pseudo-hoops. In: Proceedings of the workshop “Theory Day in Computer Science (DACS 2014)”, Analele Universitatii Bucuresti, Informatica, Anul LXI, pp 105–115Google Scholar
  6. Cignoli R, Esteva F, Godo L, Torrens A (2000) Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Comput 4:106–112CrossRefGoogle Scholar
  7. Di Nola A, Georgescu G, Iorgulescu A (2002a) Pseudo-BL algebras I. Mult-Valued Log 8:673–714Google Scholar
  8. Di Nola A, Georgescu G, Iorgulescu A (2002b) Pseudo-BL algebras II. Mult-Valued Log 8:715–750Google Scholar
  9. Dvurecenskij A (2007a) Agliano–Montagna type decomposition of linear pseudo-hoops and its applications. J Pure Appl Algebra 211:851–861Google Scholar
  10. Dvurecenskij A (2007b) Every linear pseudo-BL algebra admits a state. Soft Comput 11:495–501Google Scholar
  11. Fuchs L (1963) Partially ordered algebraic systems. Pergamon Press, New YorkMATHGoogle Scholar
  12. Georgescu G, Iorgulescu A (2001) Pseudo-MV algebras. Mult-Valued Log 6:95–135MathSciNetMATHGoogle Scholar
  13. Georgescu G, Leustean L, Preoteasa V (2005) Pseudo-hoops. J Mult-Valued Log Soft Comput 11:153–184MathSciNetMATHGoogle Scholar
  14. Hájek P (1998) Basic fuzzy logic and BL-algebras. Soft Comput 2:124–128CrossRefGoogle Scholar
  15. Laskowski MC, Shashoua YD (2002) A classification of BL-algebras. Fuzzy Sets Syst 131:271–282MathSciNetCrossRefMATHGoogle Scholar
  16. Mostert PS, Shields AL (1957) On the structure of semigroups on a compact manifold with boundary. Ann Math 65:117–143MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and CSUniversity of BucharestBucharestRomania

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