Soft Computing

, Volume 21, Issue 20, pp 6063–6071 | Cite as

Generalized state operators on residuated lattices

Foundations
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Abstract

We give a definition of a generalized state operator (g-state operator) \(\sigma \) on a residuated lattice X and a g-state residuated lattice \((X,\sigma )\), by which the class of all g-state residuated lattices is proved to be a variety, and consider properties of g-state residuated lattices. We prove some fundamental results about them, such as characterizations of \(\sigma \)-filters, extended \(\sigma \)-filters, homomorphism theorems for g-state residuated lattices. Moreover, we show that every g-state residuated lattice is a subdirect product of subdirectly irreducible g-state residuated lattices.

Keywords

(Generalized) state filters Extended filters Residuated lattices 

Notes

Acknowledgments

This study was funded by JSPS KAKENHI (Grant Number 15K00024).

Compliance with ethical standards

Conflicts of interest

The author declares that he has no conflict of interest.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Tokyo Denki UniversityTokyoJapan

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