zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Generalized rough set models. (English) Zbl 0946.68137
Polkowski, Lech (ed.) et al., Rough sets in knowledge discovery 1. Methodology and applications. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 18, 286-318 (1998).
From the introduction: This paper is a sequel of the review by Y. Y. Yao, S. K. M. Wong and T. Y. Lin [A review of rough set models. T. Y. Lin (ed.) et al., Rough sets and data mining: analysis of imprecise data. Selected papers presented at a workshop of the 1995 ACM computer science conference, CSC ’95. Boston, MA: Kluwer Academic Publishers. 47-75 (1997; Zbl 0861.68101)]. We present some new results on generalized rough set models from both the constructive and the algebraic point of view. The rest of the paper is organized as follows. From Section 2 to 5, we concentrate on an operator-oriented view of rough sets. In Section 2, we review a constructive method of rough set theory, which builds approximation operators from binary relations. In Section 3, we introduce and examine alternative representations of approximation operators, and transformations from one to another. In Section 4, we present an algebraic method of rough set theory. Axioms for approximation operators are studied. In Section 5, we study the connections between the theory of rough sets and other related theories of uncertainty. Two special classes of rough set models are studied. They are related to belief and plausibility functions, and necessity and possibility functions, respectively. Section 6 deals with a set-oriented view of rough sets based on probabilistic rough set models and rough membership functions. It enables us to draw connections between rough sets and fuzzy sets. The notion of interval rough membership functions is introduced. For simplicity, we restrict our discussion to finite and nonempty universes. Some of the results may not necessarily hold for infinite universes.
MSC:
68T30Knowledge representation