35,594 research outputs found
Implementing imperfect information in fuzzy databases
Information in real-world applications is often
vague, imprecise and uncertain. Ignoring the inherent imperfect
nature of real-world will undoubtedly introduce some deformation of human perception of real-world and may eliminate several
substantial information, which may be very useful in several
data-intensive applications. In database context, several fuzzy
database models have been proposed. In these works, fuzziness
is introduced at different levels. Common to all these proposals is
the support of fuzziness at the attribute level. This paper proposes
first a rich set of data types devoted to model the different kinds
of imperfect information. The paper then proposes a formal
approach to implement these data types. The proposed approach
was implemented within a relational object database model but it
is generic enough to be incorporated into other database models.ou
Conceptual design and implementation of the fuzzy semantic model
FSM is one of few database models that support
fuzziness, uncertainty and impreciseness of real-world at the class
definition level. FSM authorizes an entity to be partially member
of its class according to a given degree of membership that reflects
the level to which the entity verifies the extent properties of this
class. This paper deals with the conceptual design of FSM and
adresses some implementation issues.ou
Generalized and Customizable Sets in R
We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions.
Unsharp Degrees of Freedom and the Generating of Symmetries
In quantum theory, real degrees of freedom are usually described by operators
which are self-adjoint. There are, however, exceptions to the rule. This is
because, in infinite dimensional Hilbert spaces, an operator is not necessarily
self-adjoint even if its expectation values are real. Instead, the operator may
be merely symmetric. Such operators are not diagonalizable - and as a
consequence they describe real degrees of freedom which display a form of
"unsharpness" or "fuzzyness". For example, there are indications that this type
of operators could arise with the description of space-time at the string or at
the Planck scale, where some form of unsharpness or fuzzyness has long been
conjectured.
A priori, however, a potential problem with merely symmetric operators is the
fact that, unlike self-adjoint operators, they do not generate unitaries - at
least not straightforwardly. Here, we show for a large class of these operators
that they do generate unitaries in a well defined way, and that these operators
even generate the entire unitary group of the Hilbert space. This shows that
merely symmetric operators, in addition to describing unsharp physical
entities, may indeed also play a r{\^o}le in the generation of symmetries, e.g.
within a fundamental theory of quantum gravity.Comment: 23 pages, LaTe
Weighted Constraints in Fuzzy Optimization
Many practical optimization problems are characterized by someflexibility in the problem constraints, where this flexibility canbe exploited for additional trade-off between improving theobjective function and satisfying the constraints. Especially indecision making, this type of flexibility could lead to workablesolutions, where the goals and the constraints specified bydifferent parties involved in the decision making are traded offagainst one another and satisfied to various degrees. Fuzzy setshave proven to be a suitable representation for modeling this typeof soft constraints. Conventionally, the fuzzy optimizationproblem in such a setting is defined as the simultaneoussatisfaction of the constraints and the goals. No additionaldistinction is assumed to exist amongst the constraints and thegoals. This report proposes an extension of this model forsatisfying the problem constraints and the goals, where preferencefor different constraints and goals can be specified by thedecision-maker. The difference in the preference for theconstraints is represented by a set of associated weight factors,which influence the nature of trade-off between improving theoptimization objectives and satisfying various constraints.Simultaneous weighted satisfaction of various criteria is modeledby using the recently proposed weighted extensions of(Archimedean) fuzzy t-norms. The weighted satisfaction of theproblem constraints and goals are demonstrated by using a simplefuzzy linear programming problem. The framework, however, is moregeneral, and it can also be applied to fuzzy mathematicalprogramming problems and multi-objective fuzzy optimization.wiskundige programmering;fuzzy sets;optimalisatie
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