30,055 research outputs found
A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators
Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators
Generalized Fuzzy Torus and its Modular Properties
We consider a generalization of the basic fuzzy torus to a fuzzy torus with
non-trivial modular parameter, based on a finite matrix algebra. We discuss the
modular properties of this fuzzy torus, and compute the matrix Laplacian for a
scalar field. In the semi-classical limit, the generalized fuzzy torus can be
used to approximate a generic commutative torus represented by two generic
vectors in the complex plane, with generic modular parameter . The
effective classical geometry and the spectrum of the Laplacian are correctly
reproduced in the limit. The spectrum of a matrix Dirac operator is also
computed.Comment: v2: discussion and references added; v3: published versio
Unifying Practical Uncertainty Representations: II. Clouds
There exist many simple tools for jointly capturing variability and
incomplete information by means of uncertainty representations. Among them are
random sets, possibility distributions, probability intervals, and the more
recent Ferson's p-boxes and Neumaier's clouds, both defined by pairs of
possibility distributions. In the companion paper, we have extensively studied
a generalized form of p-box and situated it with respect to other models . This
paper focuses on the links between clouds and other representations.
Generalized p-boxes are shown to be clouds with comonotonic distributions. In
general, clouds cannot always be represented by random sets, in fact not even
by 2-monotone (convex) capacities.Comment: 30 pages, 7 figures, Pre-print of journal paper to be published in
International Journal of Approximate Reasoning (with expanded section
concerning clouds and probability intervals
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