Abstract
The approximation of fuzzy languages is one of the important problems, it is more practical to consider its approximate implementation if the fuzzy languages cannot be realized by a automaton. In this paper, for a real number \(\lambda \in [0,1]\), we give the definition of fuzzy \(\lambda \)-approximate context-free languages and their Pumping lemma. Then we study the algebraic properties of fuzzy \(\lambda \)-approximate context-free languages. Firstly, we give a hierarchical characterization of fuzzy \(\lambda \)-approximate context-free languages different from the previous fuzzy languages. Furthermore, we show that fuzzy \(\lambda \)-approximate context-free languages are closed under the operations union, concatenation and Kleene closure, but not closed under the operations intersection, complement, Łukasiewicz addition, Łukasiewicz product and Łukasiewicz implication. Finally, we discuss the relationships between fuzzy \(\lambda \)-approximate context-free languages and fuzzy \(\lambda \)-approximate regular languages, and prove that the intersection of a fuzzy \(\lambda \)-approximate context-free languages and a fuzzy \(\lambda \)-approximate regular languages is a fuzzy \(\lambda \)-approxi-mate context-free languages.
Supported by the National Natural Science Foundation of China [grant numbers 61673250]; the Fundamental Research Funds for the Central Universities [grant number Gk201803008]; and the China CEE 410 University Joint Education Project [grant number 202008].
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Acknowledgements
This work was supported by the National Natural Science Foundation of China [grant numbers 61673250]; the Fundamental Research Funds for the Central Universities [grant number Gk201803008]; and the China CEE 410 University Joint Education Project [grant number 202008].
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Li, P., Sun, H., He, Y., Yang, Y. (2022). Properties of Fuzzy \(\lambda \)-Approximate Context-Free Languages. In: Chen, Y., Zhang, S. (eds) Artificial Intelligence Logic and Applications. AILA 2022 2022. Communications in Computer and Information Science, vol 1657. Springer, Singapore. https://doi.org/10.1007/978-981-19-7510-3_9
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