Abstract
In this paper, based on complete residuated lattices, the properties of fuzzy \(Z_{L}\)-continuous posets and fuzzy \(Z_{L}\)-algebraic posets are investigated. Then we show that the set of fuzzy \(Z_{L}\)-ideals on the set of all compact elements of a fuzzy \(Z_{L}\)-algebraic poset is a fuzzy \(Z_{L}\)-closure system. Also, we prove that the image of a (strongly) fuzzy \(Z_{L}\)-continuous poset under a fuzzy \(Z_{L}\)-morphism is (strongly) fuzzy \(Z_{L}\)-continuous.
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Acknowledgements
This study was funded by the National Natural Science Foundation of China (Grant Nos. 11531009, 11501343) and the Fundamental Research Funds for the Central Universities (Grant No. GK201501001).
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Communicated by A. Di Nola.
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Ma, N., Zhao, B. Some results on fuzzy \(Z_{L}\)-continuous(algebraic) poset. Soft Comput 22, 4549–4559 (2018). https://doi.org/10.1007/s00500-017-2924-9
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DOI: https://doi.org/10.1007/s00500-017-2924-9