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Generalized state operators on residuated lattices

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. Tokyo Denki University, Tokyo, Japan

    Michiro Kondo

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  1. Michiro Kondo
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Correspondence to Michiro Kondo.

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The author declares that he has no conflict of interest.

Additional information

Communicated by A. Di Nola.

This work was partly supported by JSPS KAKENHI Grant Number 15K00024.

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Kondo, M. Generalized state operators on residuated lattices. Soft Comput 21, 6063–6071 (2017). https://doi.org/10.1007/s00500-016-2324-6

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  • DOI: https://doi.org/10.1007/s00500-016-2324-6

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