Maximum entropy approach to fuzzy control

For the same expert knowledge, if one uses different &- and V-operations in a fuzzy control methodology, one ends up with different control strategies. Each choice of these operations restricts the set of possible control strategies. Since a wrong choice can lead to a low quality control, it is reasonable to try to loose as few possibilities as possible. This idea is formalized and it is shown that it leads to the choice of min(a + b,1) for V and min(a,b) for &. This choice was tried on NASA Shuttle simulator; it leads to a maximally stable control

Uncertainty reasoning in expert systems

Intelligent control is a very successful way to transform the expert's knowledge of the type 'if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible' into an actual control. To apply this transformation, one must choose appropriate methods for reasoning with uncertainty, i.e., one must: (1) choose the representation for words like 'small', 'big'; (2) choose operations corresponding to 'and' and 'or'; (3) choose a method that transforms the resulting uncertain control recommendations into a precise control strategy. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From a mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. In this project, a new mathematical formalism (based on group theory) is developed that allows us to solve the problem of optimal choice and thus: (1) explain why the existing choices are really the best (in some situations); (2) explain a rather mysterious fact that fuzzy control (i.e., control based on the experts' knowledge) is often better than the control by these same experts; and (3) give choice recommendations for the cases when traditional choices do not work

The Effects of International F/X Markets on Domestic Currencies Using Wavelet Networks: Evidence from Emerging Markets

This paper proposes a powerful methodology wavelet networks to investigate the effects of international F/X markets on emerging markets currencies. We used EUR/USD parity as input indicator (international F/X markets) and three emerging markets currencies as Brazilian Real, Turkish Lira and Russian Ruble as output indicator (emerging markets currency). We test if the effects of international F/X markets change across different timescale. Using wavelet networks, we showed that the effects of international F/X markets increase with higher timescale. This evidence shows that the causality of international F/X markets on emerging markets should be tested based on 64-128 days effect. We also find that the effects of EUR/USD parity on Turkish Lira is higher on 17-32 days and 65-128 days scales and this evidence shows that Turkish lira is less stable compare to other emerging markets currencies as international F/X markets effects Turkish lira on shorten time scale.F/X Markets; Emerging markets; Wavelet networks; Wavelets; Neural networks

The Effects of International F/X Markets on Domestic Currencies Using Wavelet Networks: Evidence from Emerging Markets

This paper proposes a powerful methodology wavelet networks to investigate the effects of international F/X markets on emerging markets currencies. We used EUR/USD parity as input indicator (international F/X markets) and three emerging markets currencies as Brazilian Real, Turkish Lira and Russian Ruble as output indicator (emerging markets currency). We test if the effects of international F/X markets change across different timescale. Using wavelet networks, we showed that the effects of international F/X markets increase with higher timescale. This evidence shows that the causality of international F/X markets on emerging markets should be tested based on 64-128 days effect. We also find that the effects of EUR/USD parity on Turkish Lira is higher on 17-32 days and 65-128 days scales and this evidence shows that Turkish lira is less stable compare to other emerging markets currencies as international F/X markets effects Turkish lira on shorten time scale

Estimating Information Amount under Uncertainty: Algorithmic Solvability and Computational Complexity

Measurement results (and, more generally, estimates) are never absolutely accurate: there is always an uncertainty, the actual value x is, in general, different from the estimate ex. Sometimes, we know the probability of different values of the estimation error ∆x def = ex − x, sometimes, we only know the interval of possible values of ∆x, sometimes, we have interval bounds on the cdf of ∆x. To compare different measuring instruments, it is desirable to know which of them brings more information – i.e., it is desirable to gauge the amount of information. For probabilistic uncertainty, this amount of information is described by Shannon’s entropy; similar measures can be developed for interval and other types of uncertainty. In this paper, we analyze the computational complexity of the problem of estimating information amount under different types of uncertainty

The Effects of International F/X Markets on Domestic Currencies Using Wavelet Networks: Evidence from Emerging Markets

This paper proposes a powerful methodology wavelet networks to investigate the effects of international F/X markets on emerging markets currencies. We used EUR/USD parity as input indicator (international F/X markets) and three emerging markets currencies as Brazilian Real, Turkish Lira and Russian Ruble as output indicator (emerging markets currency). We test if the effects of international F/X markets change across different timescale. Using wavelet networks, we showed that the effects of international F/X markets increase with higher timescale. This evidence shows that the causality of international F/X markets on emerging markets should be tested based on 64-128 days effect. We also find that the effects of EUR/USD parity on Turkish Lira is higher on 17-32 days and 65-128 days scales and this evidence shows that Turkish lira is less stable compare to other emerging markets currencies as international F/X markets effects Turkish lira on shorten time scale

Maximum entropy approach to fuzzy control

Traditional control theory helps only in the situations when we know the behavior of the system that we are going to control. However, in many situations, e.g., in space exploration, we do not have this knowledge, but we still have to make control decisions. In such situations, a reasonable idea is to find an operator who is good in this kind of control

MAXIMUM ENTROPY APPROACH TO FUZZY CONTROL

1. INTRODUCTION Traditional control theory helps only in the situations when we know the behavior of the system that we are going to control. However, in many situations, e.g., in space exploration, we do not have this knowledge, but we still have to make control decisions. In such situations, a reasonable idea is to find an operator who is good in this kind of control, and translate his control experience into a precise formula. This control experience is not usually formulated in terms of the natural-language rules like "if x is small, then control must also be small". The methodology of translating these rules into an actual control strategy was proposed by L. Zadeh under the name of fuzzy control [CZ72, M74] (for a survey see, e.g., [L90])