8,309 research outputs found
Conditional operations on fuzzy numbers
An estimate of a joint possibility distribution of two fuzzy numbers, based on fuzzy relations with a third fuzzy variable, is suggested. This leads to the operations of conditional addition and conditional multiplication, of interactive fuzzy numbers for which joint possibility distributions with a fuzzy variable are known
Tracking uncertainty in a spatially explicit susceptible-infected epidemic model
In this paper we conceive an interval-valued continuous cellular automaton for describing the spatio-temporal dynamics of an epidemic, in which the magnitude of the initial outbreak and/or the epidemic properties are only imprecisely known. In contrast to well-established approaches that rely on probability distributions for keeping track of the uncertainty in spatio-temporal models, we resort to an interval representation of uncertainty. Such an approach lowers the amount of computing power that is needed to run model simulations, and reduces the need for data that are indispensable for constructing the probability distributions upon which other paradigms are based
Characterizing matrices with -simple image eigenspace in max-min semiring
A matrix is said to have -simple image eigenspace if any eigenvector
belonging to the interval is the unique solution of the system in
. The main result of this paper is a combinatorial characterization of such
matrices in the linear algebra over max-min (fuzzy) semiring.
The characterized property is related to and motivated by the general
development of tropical linear algebra and interval analysis, as well as the
notions of simple image set and weak robustness (or weak stability) that have
been studied in max-min and max-plus algebras.Comment: 23 page
Interval LU-fuzzy arithmetic in the Black and Scholes option pricing
In financial markets people have to cope with a lot of uncertainty while making decisions. Many models have been introduced in the last years to handle vagueness but it is very difficult to capture together all the fundamental characteristics of real markets. Fuzzy modeling for finance seems to have some challenging features describing the financial markets behavior; in this paper we show that the vagueness induced by the fuzzy mathematics can be relevant in modelling objects in finance, especially when a flexible parametrization is adopted to represent the fuzzy numbers. Fuzzy calculus for financial applications requires a big amount of computations and the LU-fuzzy representation produces good results due to the fact that it is computationally fast and it reproduces the essential quality of the shape of fuzzy numbers involved in computations. The paper considers the Black and Scholes option pricing formula, as long as many other have done in the last few years. We suggest the use of the LU-fuzzy parametric representation for fuzzy numbers, introduced in Guerra and Stefanini and improved in Stefanini, Sorini and Guerra, in the framework of the Black and Scholes model for option pricing, everywhere recognized as a benchmark; the details of the computations by the interval fuzzy arithmetic approach and an illustrative example are also incuded.Fuzzy Operations, Option Pricing, Black and Scholes
A class of fuzzy numbers induced by probability density functions and their arithmetic operations
In this paper we are interested in a class of fuzzy numbers which is uniquely
identified by their membership functions. The function space, denoted by , will be constructed by combining a class of nonlinear mappings
(subjective perception) and a class of probability density functions (PDF)
(objective entity), respectively. Under our assumptions, we prove that there
always exists a class of to fulfill the observed outcome for a given class
of . Especially, we prove that the common triangular number can be
interpreted by a function pair . As an example, we consider a sample
function space where is the tangent function and is chosen
as the Gaussian kernel with free variable . By means of the free variable
(which is also the expectation of ), we define the addition,
scalar multiplication and subtraction on . We claim that, under our
definitions, has a linear algebra. Some numerical examples are
provided to illustrate the proposed approach
Uncertainty-Aware Principal Component Analysis
We present a technique to perform dimensionality reduction on data that is
subject to uncertainty. Our method is a generalization of traditional principal
component analysis (PCA) to multivariate probability distributions. In
comparison to non-linear methods, linear dimensionality reduction techniques
have the advantage that the characteristics of such probability distributions
remain intact after projection. We derive a representation of the PCA sample
covariance matrix that respects potential uncertainty in each of the inputs,
building the mathematical foundation of our new method: uncertainty-aware PCA.
In addition to the accuracy and performance gained by our approach over
sampling-based strategies, our formulation allows us to perform sensitivity
analysis with regard to the uncertainty in the data. For this, we propose
factor traces as a novel visualization that enables to better understand the
influence of uncertainty on the chosen principal components. We provide
multiple examples of our technique using real-world datasets. As a special
case, we show how to propagate multivariate normal distributions through PCA in
closed form. Furthermore, we discuss extensions and limitations of our
approach
- …