The decomposition of linearly ordered pseudo-hoops
- 64 Downloads
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.
KeywordsNon-commutative fuzzy logic Pseudo-hoops Ordinal sum decomposition
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.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Ceterchi R (2012) The Decomposition of linearly ordered pseudo-hoops. In: LATD 2012, 10–14 September 2012, Kanazawa, Ishikawa, JapanGoogle Scholar
- 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
- Di Nola A, Georgescu G, Iorgulescu A (2002a) Pseudo-BL algebras I. Mult-Valued Log 8:673–714Google Scholar
- Di Nola A, Georgescu G, Iorgulescu A (2002b) Pseudo-BL algebras II. Mult-Valued Log 8:715–750Google Scholar
- Dvurecenskij A (2007a) Agliano–Montagna type decomposition of linear pseudo-hoops and its applications. J Pure Appl Algebra 211:851–861Google Scholar
- Dvurecenskij A (2007b) Every linear pseudo-BL algebra admits a state. Soft Comput 11:495–501Google Scholar