MV-pairs and state operators

Pulmannová, Sylvia; Vinceková, Elena

doi:10.1016/j.fss.2014.04.002

Cited by 4 publications

(1 citation statement)

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“…Such a state is called an internal state or a state operator. For detailed investigations, see Borzooei, Dvurecenskij, and Zahiri (2014), Botur and Dvurecenskij (2013), Ciungu, Dvurecenskij, and Hyčko (2011), Dvurecenskij (2001), Flaminio and Montagna 2007, He, Xin, and Yang 2015, Jencová and Pulmannová (2015, Di Nola and Dvurecenskij (2009), Di Nola, Dvurecenskij, and Lettieri (2010), Pulmannová and Vinceková (2015), Rachůnek and Salounova (2011).…”

Section: Introductionmentioning

confidence: 99%

Hybrid generalized Bosbach and Rie c̆ an states on non-commutative residuated lattices

Yang²

2016

International Journal of General Systems

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Generalized Bosbach and Riecan states, which are useful for the development of an algebraic theory of probabilistic models for commutative or non-commutative fuzzy logics, have been investigated in the literature. In this paper, a new way arising from generalizing residuated lattice-based filters from commutative case to non-commutative one is applied to introduce new notions of generalized Bosbach and Riecan states, which are called hybrid ones, on non-commutative residuated lattices is provided, and the relationships between hybrid generalized states and those existing ones are studied, examples show that they are different. In particular, two problems from L.C. Ciungu, G. Georgescu, and C. Mure, "Generalized Bosbach States: Part I" (Archive for Mathematical Logic 52 (2013): 335-376) are solved, and properties of hybrid generalized states, which are similar to those on commutative residuated lattices, are obtained without the condition "strong". ARTICLE HISTORY

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