States, state operators and quasi-pseudo-MV algebras

Chen, Wenjuan; Dudek, Wiesław A.

doi:10.1007/s00500-018-3069-1

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2019

2022

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“…It is known that the notion of state was firstly defined on an MV-algebra by Kõpka and Chovane in [32], and then has been studied and applied to other algebraic structures, since they have important roles in studying logical algebras (see, for instance, Borzooei et al [3,4,5], Buşneag [8,9], Ciungu [13,14,15], Ciungu and Dvurečenskij [17], Ciungu et al [16,18], Chen and Dudek [10], Cheng et al [11], Di Nola and Dvurečenskij [21], Di Nola et al [22], Dvurečenskij and Zahiri https://doi.org/10.52547/HATEF.JAHLA. 3.3.4 (vi) if x * y = z, then z * y = z and y * z = y, (vii) if (x * y) * (z * u) = (x * z) * (y * u), then X = {0}.…”

Section: Introductionmentioning

confidence: 99%

Applications of states to BI-algebras

Rezaei

Soleymani

2022

JAHLA

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This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebras. We define state ideals on BI-algebras and give a characterization of the least state ideal of a BI-algebra. It is proved that the kernel of a Bosbach state on a BI-algebra X is an ideal of X. Further, by these concepts, we introduce the notions of state BI-algebras and state-morphism BIalgebras. The notion of complement pairs of a BI-algebra X is defined, and proves that under suitable conditions, there is a one-to-one correspondence between complement pairs of BI-algebras and state-morphism operators on BI-algebras.

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