zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Relational interpretations of neighborhood operators and rough set approximation operators. (English) Zbl 0949.68144
The author presents a generalization of the rough set approach by introducing neighborhood systems defined by binary relations. For each object of the universe of such a system a nonempty family of subsets of the universe is associated. Some relationships with modal logic are summarized. The neighborhood systems are then used to define and study the basic properties of set approximations.

68T37Reasoning under uncertainty
03E72Fuzzy set theory
68T27Logic in artificial intelligence
Full Text: DOI
[1] Chellas, B. F.: Modal logic: an introduction. (1980) · Zbl 0431.03009
[2] Cohn, P. M.: Universal algebra. (1965) · Zbl 0141.01002
[3] Koczy, L. T.: Review of ”on a concept of rough sets” by zakowski. Mathematical review 84i, 03092 (1984)
[4] Lin, T. Y.: Neighborhood systems and relational database. Proceedings of CSC’88 (1988)
[5] Lin, T. Y.: Neighborhood systems and approximation in database and knowledge base systems. Proceedings of the fourth international symposium on methodologies of intelligent systems, poster session (1989)
[6] Lin, T. Y.: Topological and fuzzy rough sets. Intelligent decision support: handbook of applications and advances of the rough sets theory, 287-304 (1992)
[7] Lin, T. Y.: Neighborhood systems -- application to qualitative fuzzy and rough sets. Advances in machine intelligence and soft-computing, 132-155 (1997)
[8] Lin, T. Y.; Liu, Q.: Rough approximate operators: axiomatic rough set theory. Rough sets, fuzzy sets and knowledge discovery, 256-260 (1994) · Zbl 0818.03028
[9] Lin, T. Y.; Liu, Q.; Huang, K. J.; Chen, W.: Rough sets, neighborhood systems and approximation. Proceedings of the fifth international symposium on methodologies of intelligent systems, 130-141 (25--27 October 1990)
[10] Lin, T. Y.; Yao, Y. Y.: Mining soft rules using rough sets and neighborhoods. Proceedings of the symposium on modelling, analysis and simulation, computational engineering in systems applications (CESA’96), IMASCS multiconference, 1095-1100 (9--12 July 1996)
[11] Orlowska, E.: Semantics of nondeterministic possible worlds. Bulletin of the Polish Academy of sciences: mathematics 33, 453-458 (1985)
[12] Orlowska, E.: Semantics analysis of inductive reasoning. Theoretical computer science 43, 81-89 (1986)
[13] Orlowska, E.: Kripke semantics for knowledge representation logics. Studia logica 49, 255-272 (1990) · Zbl 0726.03023
[14] Pawlak, Z.: Rough sets. International journal of computer and information science 11, 341-356 (1982) · Zbl 0501.68053
[15] Pawlak, Z.: Rough classification. International journal of man-machine studies 20, 469-483 (1984) · Zbl 0541.68077
[16] Pawlak, Z.: Rough sets: A new approach to vagueness. Fuzzy logic for the management of uncertainty, 105-118 (1992)
[17] Pawlak, Z.: Hard and soft sets. Rough sets, fuzzy sets and knowledge discovery, 130-135 (1994) · Zbl 0819.04008
[18] Pomykala, J. A.: Approximation operations in approximation space. Bulletin of the Polish Academy of sciences: mathematics 35, 653-662 (1987)
[19] Pomykala, J. A.: On definability in the nondeterministic information system. Bulletin of the Polish Academy of sciences: mathematics 36, 193-210 (1988)
[20] Sierpenski, W.; Krieger, C.: General topology. (1956)
[21] Slowinski, R.; Vanderpooten, D.: Similarity relation as a basis for rough approximations. Advances in machine intelligence and soft-computing, 17-33 (1997)
[22] Wasilewska, A.: Conditional knowledge representation systems -- model for an implementation. Bulletin of the Polish Academy of sciences: mathematics 37, 63-69 (1987)
[23] Wong, S. K. M.; Yao, Y. Y.: Roughness theory. Proceedings of the sixth international conference on information processing and management of uncertainty in knowledge-based systems, 877-883 (1--5 July 1996)
[24] Wybraniec-Skardowska, U.: On a generalization of approximation space. Bulletin of the Polish Academy of sciences: mathematics 37, 51-61 (1989) · Zbl 0755.04011
[25] Yao, Y. Y.: Two views of the theory of rough sets in finite universes. International journal of approximate reasoning 15, 291-317 (1996) · Zbl 0935.03063
[26] Yao, Y. Y.; Lin, T. Y.: Generalization of rough sets using modal logic. Intelligent automation and soft computing, an international journal 2, 103-120 (1996)
[27] Zakowski, W.: Approximations in the space $(U, {\pi})$. Demonstratio Mathematica 16, 761-769 (1983) · Zbl 0553.04002