On residuated lattices with left and right internal state

Saeed Rasouli,Zeinab Zarin

doi:10.1016/j.fss.2019.03.001

On residuated lattices with left and right internal state

Saeed Rasouli, Zeinab Zarin

https://doi.org/10.1016/j.fss.2019.03.001

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Journal: Fuzzy Sets and Systems	Publication Date: Mar 12, 2019
Citations: 7

Affiliation: Shahid Sattari University of Aeronautical Engineering, Persian Gulf University

#Galois Connection #Internal State + Show 5 more

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Abstract

In this paper, notions of left- and right-state operators on residuated lattices are introduced and some related properties of such operators are investigated. Filters and normal filters generated by a subset in a state residuated lattice are characterized and it is shown that the lattice of filters forms a frame. Subdirectly irreducible state residuated lattices are characterized. The notion of state coannihilator is introduced and a connection between them and Galois connection is established. Finally, it is shown that the set of state coannihilators forms a complete Boolean algebra.

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