Abstract
The purpose of this paper is to study fuzzy operators induced by fuzzy relations and fuzzy relations induced by fuzzy operators. Many results are obtained about the relationship between \(*\)-preorders and fuzzy consequences operators for a fixed t-norm \(*\). We analyse these properties by considering a semi-copula (generalization of t-norm concept) instead of a t-norm. Moreover, we show that the conditions imposed cannot be relaxed. We have been able to prove some important results about the relationships between fuzzy relations and fuzzy operators in this more general context.
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Acknowledgements
The authors acknowledge the financial support of the Spanish Ministerio de Economía y Competitividad (Grant TIN2014-59543-P and Grant MTM 2016-79422-P) and Carlos Bejines also thanks the support of the Asociación de Amigos of the University of Navarra.
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Bejines, C., Chasco, M.J., Elorza, J., Montes, S. (2018). Some Results About Fuzzy Consequence Operators and Fuzzy Preorders Using Conjunctors. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_26
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DOI: https://doi.org/10.1007/978-3-319-59306-7_26
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