Measures of general fuzzy rough sets on a probabilistic space

Chen, Degang; Yang, Wenxia; Li, Fachao

doi:10.1016/j.ins.2008.03.020

Cited by 42 publications

(14 citation statements)

References 25 publications

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“…Therefore, theoretical foundations for reasoning algorithms of more expressive rough description logics including approximate concepts, number restrictions, nominals, inverse roles and role hierarchies are provided by the RDL AC . As far as future directions are concerned, these will include the approximate concept satisfiability and approximate concepts rough subsumption reasoning algorithms of rough description logics including number restrictions, nominals, inverse roles and role hierarchies, and an integration between approximate concepts and fuzzy DLs [17,41,42] or probabilistic DLs [12,28] based on fuzzy rough set theory [27,30,43,50,51] or probabilistic rough set theory [7,45,52], respectively. Furthermore, additional research effort can be focused on the investigation of the construction of approximate ontologies (or rough TBoxes) using formal concept analysis.…”

Section: Resultsmentioning

confidence: 99%

Reasoning with rough description logics: An approximate concepts approach

Jiang

Wang

Tang

et al. 2009

Information Sciences

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a b s t r a c tThe current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in description logics are analyzed in this paper. Approximate concepts are introduced to description logics based on rough set theory, and a kind of new rough description logic RDL AC (rough description logic based on approximate concepts) is proposed based on approximate concepts. The syntax, semantics and properties of the RDL AC are given. It is proved that the approximate concept satisfiability (definitely satisfiability and possibly satisfiability) reasoning problem and approximate concepts rough subsumption reasoning problem w.r.t. rough TBox in RDL AC may be reduced to the concept satisfiability reasoning problem in (almost) standard ALC (the description logic that provides the Boolean concept constructors plus the existential and universal restriction constructors). The works of this paper provide logic foundations for approximate ontologies and theoretical foundations for reasoning algorithms of more expressive rough description logics including approximate concepts, number restrictions, nominals, inverse roles and role hierarchies.

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Section: Resultsmentioning

confidence: 99%

Reasoning with rough description logics: An approximate concepts approach

Jiang

Wang

Tang

et al. 2009

Information Sciences

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“…Mô hình này là sự mở rộng mô hình Pawlak và có thể áp dụng cho cả dữ liệu giá trị thực, tuy nhiên về bản chất nó cũng giống như mô hình của Pawlak, do đó cũng gặp phải vấn đề vừa nêu trên. Trong [4] Chen và cộng sự cũng đã đề nghị một mô hình dựa trên các tập thô mờ, trong đó độ phụ thuộc được tính toán theo một quan hệ T-tương tự mờ. Tuy nhiên, mô hình này trở thành mô hình giống như mô hình Pawlak khi quan hệ T-tương tự mờ là quan hệ tương tự rõ.…”

Section: Mở đầUunclassified

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Huy¹,

Trường²,

Đức³

et al. 2016

Fair - Nghiên Cứu Cơ Bản Và Ứng Dụng Công Nghệ Thông Tin 2015

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“…Regarding the extension of rough set theory, there are several kinds of extensions of rough set theory such as probabilistic rough set theory [14,69,73] other than fuzzy rough set theory [18,19,43,52,67]. Therefore, a path for future research is an integration between the theories of probabilistic DLs [31,44] and rough DLs [54] based on probabilistic rough set theory [14,69,73].…”

Section: Thorem 8 For Any Concept C and D In L-frdls Their Lower Anmentioning

confidence: 99%

Reasoning within expressive fuzzy rough description logics

Jiang

Wang

Pei-min

et al. 2009

Fuzzy Sets and Systems

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It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledgebased applications. Description Logics (DLs) are suitable, well-known logics for managing structured knowledge that have gained considerable attention the last decade. The current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in DLs are analyzed in this paper. An integration between the theories of fuzzy DLs and rough DLs has been attempted by providing fuzzy rough DLs based on fuzzy rough set theory. The syntax, semantics and properties of fuzzy rough DLs are given. It is proved that the satisfiability, subsumption, entailment and ABox consistency reasoning in fuzzy rough DLs may be reduced to the ABox consistency reasoning in the corresponding fuzzy DLs.

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Measures of general fuzzy rough sets on a probabilistic space

Cited by 42 publications

References 25 publications

Reasoning with rough description logics: An approximate concepts approach

Reasoning with rough description logics: An approximate concepts approach

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Reasoning within expressive fuzzy rough description logics

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