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Soft Computing Explains Heuristic Numerical Methods in Data Processing and in Logic Programming
 in Data Processing and in Logic Programming
, 1997
"... We show that fuzzy logic and other soft computing approaches explain and justify heuristic numerical methods used in data processing and in logic programming, in particular, Mmethods in robust statistics, regularization techniques, metric fixed point theorems, etc. Introduction What is soft compu ..."
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We show that fuzzy logic and other soft computing approaches explain and justify heuristic numerical methods used in data processing and in logic programming, in particular, Mmethods in robust statistics, regularization techniques, metric fixed point theorems, etc. Introduction What is soft computing good for? Traditional viewpoint. When are soft computing methods (fuzzy, neural, etc.) mostly used now? Let us take, as an example, control, which is one of the major success stories of soft computing (especially of fuzzy methods; see, e.g., (Klir 1995)). ffl In control, if we know the exact equations that describe the controlled system, and if we know the exact objective function of the control, then we can often apply the optimal control techniques developed in traditional (crisp) control theory and compute the optimal control. Even in these situations, we can, in principle, use soft computing methods instead: e.g., we can use simpler fuzzy control rules instead of (more complicated...
Possible New Directions in Mathematical Foundations of Fuzzy Technology: A Contribution to the Mathematics of Fuzzy Theory
 Proceedings of the VietnamJapan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September2nd
, 1998
"... this paper, we describe new possible applicationoriented directions towards formalizing these new ideas: ..."
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Cited by 7 (7 self)
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this paper, we describe new possible applicationoriented directions towards formalizing these new ideas:
Title: A RiskMetric Framework for Enterprise Risk Management
"... Abstract: A riskmetric framework that supports Enterprise Risk Management is described. At the heart of the framework is the notion of a risk profile that provides risk measurement for risk elements. By providing a generic template in which metrics can be codified in terms of metric space operators ..."
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Abstract: A riskmetric framework that supports Enterprise Risk Management is described. At the heart of the framework is the notion of a risk profile that provides risk measurement for risk elements. By providing a generic template in which metrics can be codified in terms of metric space operators, risk profiles can be used to construct a variety of risk measures for different business contexts. These measures can vary from conventional economic risk calculations to the kinds of metrics that are used by decision support systems, such as those supporting inexact reasoning and which are considered to closely match how humans combine information. 1
How to Interpret Neural Networks In Terms of Fuzzy Logic?
, 2001
"... Neural networks are a very efficient learning tool, e.g., for transforming an experience of an expert human controller into the design of an automatic controller. It is desirable to reformulate the neural network expression for the inputoutput function in terms most understandable to an expert cont ..."
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Neural networks are a very efficient learning tool, e.g., for transforming an experience of an expert human controller into the design of an automatic controller. It is desirable to reformulate the neural network expression for the inputoutput function in terms most understandable to an expert controller, i.e., by using words from natural language. There are several methodologies for transforming such naturallanguage knowledge into a precise form; since these methodologies have to take into consideration the uncertainty (fuzziness) of natural language, they are usually called fuzzy logics. 1
PROPERTIES OF FUZZY LOGICAL OPERATIONS
, 2009
"... This thesis deals with geometrical and differential properties of triangular norms (tnorms for short), i.e. binary operations which implement logical conjunctions in fuzzy logic. It is divided into two main parts. The first part discusses the problem of a visual characterization of the associativit ..."
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This thesis deals with geometrical and differential properties of triangular norms (tnorms for short), i.e. binary operations which implement logical conjunctions in fuzzy logic. It is divided into two main parts. The first part discusses the problem of a visual characterization of the associativity of tnorms. The thesis adopts the results given by web geometry, mainly the concept of the Reidemeister closure condition, in order to characterize the shape of level sets of tnorms. This way, a visual characterization of the associativity is provided for general, continuous, and continuous Archimedean tnorms. The second part of the thesis deals with differential properties of continuous Archimedean tnorms. It is shown that partial derivatives of such a tnorm on a particular subset of its domain correspond directly to the generator (or to the derivative of the generator) of the tnorm. Namely, partial derivatives of tnorms along the annihilator, the unit element, a level set, and a vertical section are studied. As the result, several methods which reconstruct
Use of Satellite Image Referencing Algorithms to Characterize Asphaltic Concrete Mixtures
, 2002
"... A natural way to test the structural integrity of a pavement is to send signals with different frequencies through the pavement and compare the results with the signals passing through an ideal pavement. For this comparison, we must determine how, for the corresponding mixture, the elasticity E depe ..."
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A natural way to test the structural integrity of a pavement is to send signals with different frequencies through the pavement and compare the results with the signals passing through an ideal pavement. For this comparison, we must determine how, for the corresponding mixture, the elasticity E depends on the frequency f in the range from 0.1 to 10 5 Hz. It is very expensive to perform measurements in high frequency area (above 20 Hz). To avoid these measurements, we can use the fact that for most of these mixtures, when we change a temperature, the new dependence changes simply by scaling. Thus, instead of performing expensive measurements for different frequencies, we can measure the dependence of E on moderate frequencies f for different temperatures, and then combine the resulting curves into a single "master" curve. In this paper, we show how fuzzy techniques can help to automate this "combination".
Uniqueness of Reconstruction for Yager’s tNorm Combination of Probabilistic and Possibilistic Knowledge
"... Often, about the same reallife system, we have both measurementrelated probabilistic information expressed by a probability measure P (S) and expertrelated possibilistic information expressed by a possibility measure M(S). To get the most adequate idea about the system, we must combine these two p ..."
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Often, about the same reallife system, we have both measurementrelated probabilistic information expressed by a probability measure P (S) and expertrelated possibilistic information expressed by a possibility measure M(S). To get the most adequate idea about the system, we must combine these two pieces of information. For this combination, R. Yager – borrowing an idea from fuzzy logic – proposed to use a tnorm f&(a, b) such as the product f&(a, b) = a · b, i.e., to consider a set function f(S) = f&(P (S), M(S)). A natural question is: can we uniquely reconstruct the two parts of knowledge from this function f(S)? In our previous paper, we showed that such a unique reconstruction is possible for the product tnorm; in this paper, we extend this result to a general class of tnorms. 1 Formulation of the Problem Need to combine probabilistic and possibilistic knowledge. In many
On the Optimal Choice of Quality Metric In Image Compression: A Soft Computing Approach
, 2000
"... Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy com ..."
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Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy compression, the reconstructed image e I is, in general, different from the original image I. There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I ; e I) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L p metrics d(I ; e I) = R jI(x) \Gamma e I(x)j p d...
Need for Data Processing Naturally Leads to Fuzzy Logic (and Neural Networks): Fuzzy Beyond Experts and Beyond Probabilities
"... Fuzzy techniques have been originally designed to describe imprecise (\fuzzy") expert knowledge. Somewhat surprisingly, fuzzy techniques have also been successfully used in situations without expert knowledge, when all we have is data. In this paper, we explain this surprising phenomenon by sh ..."
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Fuzzy techniques have been originally designed to describe imprecise (\fuzzy") expert knowledge. Somewhat surprisingly, fuzzy techniques have also been successfully used in situations without expert knowledge, when all we have is data. In this paper, we explain this surprising phenomenon by showing that the need for optimal processing of data (including crisp data) naturally leads to fuzzy and neural data processing techniques. This result shows the potential of fuzzy data processing. To maximally utilize this potential, we need to provide an operational meaning of the corresponding fuzzy degrees. We show that such a meaning can be extracted from the above justication of fuzzy techniques. It turns
On the Optimal Choice of Quality Metric In Image Compression: A Soft Computing Approach
, 2000
"... Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy com ..."
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Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy compression, the reconstructed image e I is, in general, different from the original image I . There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I ; e I) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L p metrics d(I ; e I) = R jI(x) \Gamma e I(x)j p d...