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Articles 61 - 78 of 78
Full-Text Articles in Physical Sciences and Mathematics
How To Take Into Account Model Inaccuracy When Estimating The Uncertainty Of The Result Of Data Processing, Vladik Kreinovich, Olga Kosheleva, Andrzej Pownuk, Rodrigo A. Romero
How To Take Into Account Model Inaccuracy When Estimating The Uncertainty Of The Result Of Data Processing, Vladik Kreinovich, Olga Kosheleva, Andrzej Pownuk, Rodrigo A. Romero
Departmental Technical Reports (CS)
In engineering design, it is important to guarantee that the values of certain quantities such as stress level, noise level, vibration level, etc., stay below a certain threshold in all possible situations, i.e., for all possible combinations of the corresponding internal and external parameters. Usually, the number of possible combinations is so large that it is not possible to physically test the system for all these combinations. Instead, we form a computer model of the system, and test this model. In this testing, we need to take into account that the computer models are usually approximate. In this paper, we …
When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu
When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu
Departmental Technical Reports (CS)
In many real-life situations, we are interested in the values of physical quantities x1, ..., xn which are difficult (or even impossible) to measure directly. To estimate these values, we measure easier-to-measure quantities y1, ..., ym which are related to the desired quantities by a known relation, and use these measurement results to estimate xi. The corresponding data processing algorithms are sometimes very complex and time-consuming, so a natural question is: are simpler (and, thus, faster) algorithms possible for solving this data processing problem? In this paper, we show that by using …
How Success In A Task Depends On The Skills Level: Two Uncertainty-Based Justifications Of A Semi-Heuristic Rasch Model, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich
How Success In A Task Depends On The Skills Level: Two Uncertainty-Based Justifications Of A Semi-Heuristic Rasch Model, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
The more skills a student acquires, the more successful this student is with the corresponding tasks. Empirical data shows that the success in a task grows as a logistic function of skills; this dependence is known as the Rasch model. In this paper, we provide two uncertainty-based justifications for this model: the first justification provides a simple fuzzy-based intuitive explanation for this model, while the second -- more complex one -- explains the exact quantitative behavior of the corresponding dependence.
How Geophysicists' Intuition Helps Seismic Data Processing, Afshin Gholamy, Vladik Kreinovich
How Geophysicists' Intuition Helps Seismic Data Processing, Afshin Gholamy, Vladik Kreinovich
Departmental Technical Reports (CS)
In geophysics, signals come with noise. It is desirable to minimize the effect of this noise. If we knew the probabilities of different values of signal and noise, we could use statistical filtering techniques. In geophysics, however, we rarely know the exact values of these probabilities; instead, we have to rely on the expertise and intuition of experts. We show how fuzzy techniques can transform this expertise into precise de-noising methods, we explain that the resulting methods indeed satisfy several natural requirements, and that these methods are in good accordance with heuristic techniques successfully used by geophysicists.
How To Speed Up Software Migration And Modernization: Successful Strategies Developed By Precisiating Expert Knowledge, Francisco Zapata, Octavio Lerma, Leobardo Valera, Vladik Kreinovich
How To Speed Up Software Migration And Modernization: Successful Strategies Developed By Precisiating Expert Knowledge, Francisco Zapata, Octavio Lerma, Leobardo Valera, Vladik Kreinovich
Departmental Technical Reports (CS)
Computers are getting faster and faster; the operating systems are getting more sophisticated. Often, these improvements necessitate that we migrate the existing software to the new platform. In the ideal world, the migrated software should run perfectly well on a new platform; however, in reality, when we try that, thousands of errors appear, errors that need correcting. As a result, software migration is usually a very time-consuming process. A natural way to speed up this process is to take into account that errors naturally fall into different categories, and often, a common correction can be applied to all error from …
Why It Is Important To Precisiate Goals, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen
Why It Is Important To Precisiate Goals, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
After Zadeh and Bellman explained how to optimize a function under fuzzy constraints, there have been many successful applications of this optimization. However, in many practical situations, it turns out to be more efficient to precisiate the objective function before performing optimization. In this paper, we provide a possible explanation for this empirical fact.
Simple Linear Interpolation Explains All Usual Choices In Fuzzy Techniques: Membership Functions, T-Norms, T-Conorms, And Defuzzification, Vladik Kreinovich, Jonathan Quijas, Esthela Gallardo, Caio De Sa Lopes, Olga Kosheleva, Shahnaz Shahbazova
Simple Linear Interpolation Explains All Usual Choices In Fuzzy Techniques: Membership Functions, T-Norms, T-Conorms, And Defuzzification, Vladik Kreinovich, Jonathan Quijas, Esthela Gallardo, Caio De Sa Lopes, Olga Kosheleva, Shahnaz Shahbazova
Departmental Technical Reports (CS)
Most applications of fuzzy techniques use piece-wise linear (triangular or trapezoid) membership functions, min or product t-norms, max or algebraic sum t-conorms, and centroid defuzzification. Similarly, most applications of interval-valued fuzzy techniques use piecewise-linear lower and upper membership functions. In this paper, we show that all these choices can be explained as applications of simple linear interpolation.
Fuzzy, Intuitionistic Fuzzy, What Next?, Vladik Kreinovich, Bui Cong Cuong
Fuzzy, Intuitionistic Fuzzy, What Next?, Vladik Kreinovich, Bui Cong Cuong
Departmental Technical Reports (CS)
In the 1980s, Krassimir Atanassov proposed an important generalization of fuzzy sets, fuzzy logic, and fuzzy techniques -- intuitionistic fuzzy approach, which provides a more accurate description of expert knowledge. In this paper, we describe a natural way how the main ideas behind the intuitionistic fuzzy approach can be expanded even further, towards an even more accurate description of experts' knowledge.
Why Sugeno Lambda-Measures, Hung T. Nguyen, Vladik Kreinovich, Joe Lorkowski, Saiful Abu
Why Sugeno Lambda-Measures, Hung T. Nguyen, Vladik Kreinovich, Joe Lorkowski, Saiful Abu
Departmental Technical Reports (CS)
To describe expert uncertainty, it is often useful to go beyond additive probability measures and use non-additive (fuzzy) measures. One of the most widely and successfully used class of such measures is the class of Sugeno lambda-measures. Their success is somewhat paradoxical, since from the purely mathematical viewpoint, these measures are -- in some reasonable sense -- equivalent to probability measures. In this paper, we explain this success by showing that while mathematically, it is possible to reduce Sugeno measures to probability measures, from the computational viewpoint, using Sugeno measures is much more efficient. We also show that among all …
Creative Discussions Or Memorization? Maybe Both? (On The Example Of Teaching Computer Science), Vladik Kreinovich, Olga Kosheleva
Creative Discussions Or Memorization? Maybe Both? (On The Example Of Teaching Computer Science), Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
We all strive to be creative in our teaching, but there is often not enough time to make all the topics creative fun. So sometimes, we teach memorization first, understanding later. We do it, but we often do it without seriously analyzing which topics to "sacrifice" to memorization. In this talk, we use simple mathematical models of learning to come up with relevant recommendations: Namely, all the topics form a dependency graph, and if we do not have enough time to allow students to treat all topics with equal creativity, then the most reasonable topics for memorization first are the …
Inverse Problems In Theory And Practice Of Measurements And Metrology, Konstantin K. Semenov, Gennadi N. Solopchenko, Vladik Kreinovich
Inverse Problems In Theory And Practice Of Measurements And Metrology, Konstantin K. Semenov, Gennadi N. Solopchenko, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we consider the role of inverse problems in metrology. We describe general methods of solving inverse problems which are useful in measurements practice. We also discuss how to modify these methods in situations in which there is a need for real-time data processing.
Minimax Portfolio Optimization Under Interval Uncertainty, Meng Yuan, Xu Lin, Junzo Watada, Vladik Kreinovich
Minimax Portfolio Optimization Under Interval Uncertainty, Meng Yuan, Xu Lin, Junzo Watada, Vladik Kreinovich
Departmental Technical Reports (CS)
In the 1950s, Markowitz proposed to combine different investment instruments to design a portfolio that either maximizes the expected return under constraints on volatility (risk) or minimizes the risk under given expected return. Markowitz's formulas are still widely used in financial practice. However, these formulas assume that we know the exact values of expected return and variance for each instrument, and that we know the exact covariance of every two instruments. In practice, we only know these values with some uncertainty. Often, we only know the bounds of these values -- i.e., in other words, we only know the intervals …
Towards The Possibility Of Objective Interval Uncertainty In Physics. Ii, Luc Longpre, Olga Kosheleva, Vladik Kreinovich
Towards The Possibility Of Objective Interval Uncertainty In Physics. Ii, Luc Longpre, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Applications of interval computations usually assume that while we only know an interval containing the actual (unknown) value of a physical quantity, there is the exact value of this quantity, and that in principle, we can get more and more accurate estimates of this value. Physicists know, however, that, due to uncertainty principle, there are limitations on how accurately we can measure the values of physical quantities. One of the important principles of modern physics is operationalism -- that a physical theory should only use observable properties. This principle is behind most successes of the 20th century physics, starting with …
When An Idea Comes, Write It Down Right Away: Mathematical Justification Of Vladimir Smirnov's Advice, Olga Kosheleva, Vladik Kreinovich
When An Idea Comes, Write It Down Right Away: Mathematical Justification Of Vladimir Smirnov's Advice, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Among several advices to students, Vladimir Smirnov, a renowned Russian mathematician, suggested that when an idea comes, it is better to write it down right away. In this paper, we provide a quantitative justification for this advice.
Optimizing Pred(25) Is Np-Hard, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Optimizing Pred(25) Is Np-Hard, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Usually, in data processing, to find the parameters of the models that best fits the data, people use the Least Squares method. One of the advantages of this method is that for linear models, it leads to an easy-to-solve system of linear equations. A limitation of this method is that even a single outlier can ruin the corresponding estimates; thus, more robust methods are needed. In particular, in software engineering, often, a more robust pred(25) method is used, in which we maximize the number of cases in which the model's prediction is within the 25% range of the observations. In …
Why Right-Brain Cultures Are More Flexible: A Possible Explanation Of Yu. Manin's Observation, Olga Kosheleva, Vladik Kreinovich
Why Right-Brain Cultures Are More Flexible: A Possible Explanation Of Yu. Manin's Observation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Yuri Manin, a renowned mathematician, observed that it is much easier for a person raised in a right-brain culture to adjust to the left-brain environment than vice versa. In this paper, we provide a possible explanation for this phenomenon.
How To Test Hypotheses When Exact Values Are Replaced By Intervals To Protect Privacy: Case Of T-Tests, Vladik Kreinovich, Christian Servin
How To Test Hypotheses When Exact Values Are Replaced By Intervals To Protect Privacy: Case Of T-Tests, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Researchers continuously look for possible relations between relevant quantities, e.g., relations which may help in preventing and curing diseases. Once a hypothesis is made about such a relation, it is necessary to test whether it is confirmed by the data. For such hypothesis testing, t-tests are most widely used. For example, a t-test can check, based on two samples, whether it is possible that they come from distributions with the same mean -- e.g., whether the average blood pressure after a proposed treatment is the same as before or it is provably smaller -- meaning that the tested treatment works. …
Why Lattice-Valued Fuzzy Values? A Mathematical Justification, Rujira Ouncharoen, Vladik Kreinovich, Hung T. Nguyen
Why Lattice-Valued Fuzzy Values? A Mathematical Justification, Rujira Ouncharoen, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
To take into account that expert's degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0,1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a theorem explaining why it is reasonable to require that the set of degrees is a lattice.