Generalized Bosbach and Riečan states on nucleus-based-Glivenko residuated lattices

Zhao, Bin; Zhou, Hongjun

doi:10.1007/s00153-013-0338-7

Cited by 8 publications

(1 citation statement)

References 28 publications

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“…In Ma and Fu (2015), several new types of generalized Bosbach states were defined, and in Ma and Yang (2015) the relationships between various generalized states and residuated lattice-based filters were investigated on commutative residuated lattices. Some further results on generalized states can be found in Ciungu, Georgescu, and Mureşan (2013), Ciungu (2014), Georgescu and Mureşan (2010), Ma and Fu (2015), Ma and Yang (2015), Zhao and Zhou (2013), Zhou and Zhao (2012).…”

Section: Introductionmentioning

confidence: 94%

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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