55,773 research outputs found
Weighted lattice polynomials
We define the concept of weighted lattice polynomial functions as lattice
polynomial functions constructed from both variables and parameters. We provide
equivalent forms of these functions in an arbitrary bounded distributive
lattice. We also show that these functions include the class of discrete Sugeno
integrals and that they are characterized by a median based decomposition
formula.Comment: Revised version (minor changes
Fuzzy modelling using a simplified rule base
Transparency and complexity are two major concerns of fuzzy rule-based systems. To improve accuracy and precision of the outputs, we need to increase the partitioning of the input space. However, this increases the number of rules exponentially, thereby increasing the complexity of the system and decreasing its transparency. The main factor behind these two issues is the conjunctive canonical form of the fuzzy rules. We present a novel method for replacing these rules with their singleton forms, and using aggregation operators to provide the mechanism for combining the crisp outputs
Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
In the previous papers, we studied the 't Hooft-Polyakov (TP) monopole
configurations in the U(2) gauge theory on the fuzzy 2-sphere,and showed that
they have nonzero topological charge in the formalism based on the
Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in
the TP monopole background, which is defined in the projected space, and
provide a meaning of the projection operator. We also extend the index theorem
to general configurations which do not satisfy the equation of motion, and show
that the configuration space can be classified into the topological sectors. We
further calculate the spectrum of the GW Dirac operator in the TP monopole
backgrounds, and consider the index theorem in these cases.Comment: Latex2e, 37 pages, 3 figure
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Investment Risk Appraisal
Standard financial techniques neglect extreme situations and regards large market shifts as too unlikely to matter. This
approach may account for what occurs most of the time in the market, but the picture it presents does not reflect the reality, as the
major events happen in the rest of the time and investors are ‘surprised’ by ‘unexpected’ market movements. An alternative fuzzy
approach permits fluctuations well beyond the probability type of uncertainty and allows one to make fewer assumptions about the
data distribution and market behaviour. Fuzzifying the present value criteria, we suggest a measure of the risk associated with each
investment opportunity and estimate the project’s robustness towards market uncertainty. The procedure is applied to thirty-five UK
companies and a neural network solution to the fuzzy criterion is provided to facilitate the decision-making process. Finally, we
discuss the grounds for classical asset pricing model revision and argue that the demand for relaxed assumptions appeals for another
approach to modelling the market environment
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Soft computing in investment appraisal
Standard financial techniques neglect extreme situations and regards large market shifts as too unlikely to matter. Such approach accounts for what occurs most of the time in the market, but does not reflect the reality, as major events happen in the rest of the time and investors are ‘surprised’ by ‘unexpected’ market movements. An
alternative fuzzy approach permits fluctuations well beyond the probability type of uncertainty and allows one to make fewer assumptions about the data distribution and market behaviour.
Fuzzifying the present value criteria, we suggest a measure of the risk associated with each investment opportunity and estimate the project’s robustness towards market uncertainty. The procedure is applied to thirty-five UK companies traded on the London Stock Exchange and a neural
network solution to the fuzzy criterion is provided to facilitate the decision-making process. Finally, we suggest a specific evolutionary algorithm to train a fuzzy neural net - the bidirectional incremental evolution will automatically identify the complexity of the problem and correspondingly adapt the parameters of the fuzzy network
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