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On residuated lattices with left and right internal state

Authors:

Zeinab ZarinAuthors Info & Claims

Volume 373, Issue C

Pages 37 - 61

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

Published: 15 October 2019 Publication History

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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Cited By

Rasouli SDehghani A(2023)Mp- and purified residuated latticesSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-022-07583-x27:1(131-148)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1007/s00500-022-07583-x
Rasouli SDehghani A(2020)Topological residuated latticesSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-020-04709-x24:5(3179-3192)Online publication date: 1-Mar-2020
https://dl.acm.org/doi/10.1007/s00500-020-04709-x

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On residuated lattices with left and right internal state

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Published In

cover image Fuzzy Sets and Systems

Fuzzy Sets and Systems Volume 373, Issue C

Oct 2019

184 pages

ISSN:0165-0114

Issue’s Table of Contents

Elsevier B.V.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 15 October 2019

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Cited By

Rasouli SDehghani A(2023)Mp- and purified residuated latticesSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-022-07583-x27:1(131-148)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1007/s00500-022-07583-x
Rasouli SDehghani A(2020)Topological residuated latticesSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-020-04709-x24:5(3179-3192)Online publication date: 1-Mar-2020
https://dl.acm.org/doi/10.1007/s00500-020-04709-x

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