Abstract
Based on the idea that the cut sets of fuzzy sets are indeed crisp, but facilitate a normative theory for formalizing fuzzy set theory, this paper introduces cut sets of the fuzzy concepts and fuzzy roles as atomic concepts and atomic roles to build \(\mathcal{EFALCH}\) , a new fuzzy extension of \(\mathcal{ALCH}\). This paper gives the definition of syntax, semantics and knowledge base of \(\mathcal{EFALCH}\) and discusses the comparison among \(\mathcal{EFALCH}\) and other fuzzy extensions of \(\mathcal{ALCH}\). In addition, this paper defines the acyclic TBox form of \(\mathcal{EFALCH}\), presents sound and complete algorithms for reasoning tasks w.r.t acyclic TBox, and proves the complexity of them is PSPACE-complete.
This work was supported in part by the NSFC (60373066, 60425206, 90412003), National Grand Fundamental Research 973 Program of China (2002CB312000), National Research Foundation for the Doctoral Program of Higher Education of China (20020286004), Excellent Ph.D. Thesis Fund of Southeast University, and Advanced Armament Research Project (51406020105JB8103).
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Li, Y., Lu, J., Xu, B., Kang, D., Jiang, J. (2005). A Fuzzy Extension of Description Logic \(\mathcal{ALCH}\) . In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds) MICAI 2005: Advances in Artificial Intelligence. MICAI 2005. Lecture Notes in Computer Science(), vol 3789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11579427_16
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DOI: https://doi.org/10.1007/11579427_16
Publisher Name: Springer, Berlin, Heidelberg
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