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Full-Text Articles in Computer Engineering

Probabilistic Graphical Models Follow Directly From Maximum Entropy, Anh H. Ly, Francisco Zapata, Olac Fuentes, Vladik Kreinovich Sep 2017

Probabilistic Graphical Models Follow Directly From Maximum Entropy, Anh H. Ly, Francisco Zapata, Olac Fuentes, Vladik Kreinovich

Departmental Technical Reports (CS)

Probabilistic graphical models are a very efficient machine learning technique. However, their only known justification is based on heuristic ideas, ideas that do not explain why exactly these models are empirically successful. It is therefore desirable to come up with a theoretical explanation for these models' empirical efficiency. At present, the only such explanation is that these models naturally emerge if we maximize the relative entropy; however, why the relative entropy should be maximized is not clear. In this paper, we show that these models can also be obtained from a more natural -- and well-justified -- idea of maximizing (absolute) entropy.


Simplest Polynomial For Which Naive (Straightforward) Interval Computations Cannot Be Exact, Olga Kosheleva, Vladik Kreinovich, Songsak Sriboonchitta Jun 2017

Simplest Polynomial For Which Naive (Straightforward) Interval Computations Cannot Be Exact, Olga Kosheleva, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

One of the main problem of interval computations is computing the range of a given function over given intervals. It is known that naive interval computations always provide an enclosure for the desired range. Sometimes -- e.g., for single use expressions -- naive interval computations compute the exact range. Sometimes, we do not get the exact range when we apply naive interval computations to the original expression, but we get the exact range if we apply naive interval computations to an equivalent reformulation of the original expression. For some other functions -- including some polynomials -- we do not get the exact range ...


Normalization-Invariant Fuzzy Logic Operations Explain Empirical Success Of Student Distributions In Describing Measurement Uncertainty, Hamza Alkhatib, Boris Kargoll, Ingo Neumann, Vladik Kreinovich Jun 2017

Normalization-Invariant Fuzzy Logic Operations Explain Empirical Success Of Student Distributions In Describing Measurement Uncertainty, Hamza Alkhatib, Boris Kargoll, Ingo Neumann, Vladik Kreinovich

Departmental Technical Reports (CS)

In engineering practice, usually measurement errors are described by normal distributions. However, in some cases, the distribution is heavy-tailed and thus, not normal. In such situations, empirical evidence shows that the Student distributions are most adequate. The corresponding recommendation -- based on empirical evidence -- is included in the International Organization for Standardization guide. In this paper, we explain this empirical fact by showing that a natural fuzzy-logic-based formalization of commonsense requirements leads exactly to the Student's distributions.


How To Gauge The Accuracy Of Fuzzy Control Recommendations: A Simple Idea, Patricia Melin, Oscar Castillo, Andrzej Pownuk, Olga Kosheleva, Vladik Kreinovich Jun 2017

How To Gauge The Accuracy Of Fuzzy Control Recommendations: A Simple Idea, Patricia Melin, Oscar Castillo, Andrzej Pownuk, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy control is based on approximate expert information, so its recommendations are also approximate. However, the traditional fuzzy control algorithms do not tell us how accurate are these recommendations. In contrast, for the probabilistic uncertainty, there is a natural measure of accuracy: namely, the standard deviation. In this paper, we show how to extend this idea from the probabilistic to fuzzy uncertainty and thus, to come up with a reasonable way to gauge the accuracy of fuzzy control recommendations.


Comparisons Of Measurement Results As Constraints On Accuracies Of Measuring Instruments: When Can We Determine The Accuracies From These Constraints?, Christian Servin, Vladik Kreinovich Jun 2015

Comparisons Of Measurement Results As Constraints On Accuracies Of Measuring Instruments: When Can We Determine The Accuracies From These Constraints?, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

For a measuring instrument, a usual way to find the probability distribution of its measurement errors is to compare its results with the results of measuring the same quantity with a much more accurate instrument. But what if we are interested in estimating the measurement accuracy of a state-of-the-art measuring instrument, for which no more accurate instrument is possible? In this paper, we show that while in general, such estimation is not possible; however, can uniquely determine the corresponding probability distributions if we have several state-of-the-art measuring instruments, and for one of them, the corresponding probability distribution is symmetric.


Fuzzy Xor Classes From Quantum Computing, Anderson Ávila, Murilo Schmalfuss, Renata Reiser, Vladik Kreinovich Jun 2015

Fuzzy Xor Classes From Quantum Computing, Anderson Ávila, Murilo Schmalfuss, Renata Reiser, Vladik Kreinovich

Departmental Technical Reports (CS)

By making use of quantum parallelism, quantum processes provide parallel modelling for fuzzy connectives and the corresponding computations of quantum states can be simultaneously performed, based on the superposition of membership degrees of an element with respect to the different fuzzy sets. Such description and modelling is mainly focussed on representable fuzzy Xor connectives and their dual constructions. So, via quantum computing not only the interpretation based on traditional quantum circuit is considered, but also the notion of quantum process in the qGM model is applied, proving an evaluation of a corresponding simulation by considering graphical interfaces of the VPE-qGM ...


Symbolic Aggregate Approximation (Sax) Under Interval Uncertainty, Chrysostomos D. Stylios, Vladik Kreinovich Apr 2015

Symbolic Aggregate Approximation (Sax) Under Interval Uncertainty, Chrysostomos D. Stylios, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we monitor a system by continuously measuring the corresponding quantities, to make sure that an abnormal deviation is detected as early as possible. Often, we do not have ready algorithms to detect abnormality, so we need to use machine learning techniques. For these techniques to be efficient, we first need to compress the data. One of the most successful methods of data compression is the technique of Symbolic Aggregate approXimation (SAX). While this technique is motivated by measurement uncertainty, it does not explicitly take this uncertainty into account. In this paper, we show that we can ...


Optimizing Cloud Use Under Interval Uncertainty, Vladik Kreinovich, Esthela Gallardo Apr 2015

Optimizing Cloud Use Under Interval Uncertainty, Vladik Kreinovich, Esthela Gallardo

Departmental Technical Reports (CS)

One of the main advantages of cloud computing is that it helps the users to save money: instead of buying a lot of computers to cover all their computations, the user can rent the computation time on the cloud to cover the rare peak spikes of computer need. From this viewpoint, it is important to find the optimal division between in-house and in-the-cloud computations. In this paper, we solve this optimization problem, both in the idealized case when we know the complete information about the costs and the user's need, and in a more realistic situation, when we only ...


Which Bio-Diversity Indices Are Most Adequate, Olga Kosheleva, Craig Tweedie, Vladik Kreinovich Apr 2015

Which Bio-Diversity Indices Are Most Adequate, Olga Kosheleva, Craig Tweedie, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main objectives of ecology is to analyze, maintain, and enhance the bio-diversity of different ecosystems. To be able to do that, we need to gauge bio-diversity. Several semi-heuristic diversity indices have been shown to be in good accordance with the intuitive notion of bio-diversity. In this paper, we provide a theoretical justification for these empirically successful techniques. Specifically, we show that the most widely used techniques -- Simpson index -- can be justified by using simple fuzzy rules, while a more elaborate justification explains all empirically successful diversity indices.


Model Reduction: Why It Is Possible And How It Can Potentially Help To Control Swarms Of Unmanned Arial Vehicles (Uavs), Martine Ceberio, Leobardo Valera, Olga Kosheleva, Rodrigo A. Romero Apr 2015

Model Reduction: Why It Is Possible And How It Can Potentially Help To Control Swarms Of Unmanned Arial Vehicles (Uavs), Martine Ceberio, Leobardo Valera, Olga Kosheleva, Rodrigo A. Romero

Departmental Technical Reports (CS)

In many application areas, such as meteorology, traffic control, etc., it is desirable to employ swarms of Unmanned Arial Vehicles (UAVs) to provide us with a good picture of the changing situation and thus, to help us make better predictions (and make better decisions based on these predictions). To avoid duplication, interference, and collisions, UAVs must coordinate their trajectories. As a result, the optimal control of each of these UAVs should depend on the positions and velocities of all others -- which makes the corresponding control problem very complicated. Since, in contrast to controlling a single UAV, the resulting problem is ...


How To Estimate Expected Shortfall When Probabilities Are Known With Interval Or Fuzzy Uncertainty, Christian Servin, Hung T. Nguyen, Vladik Kreinovich Apr 2015

How To Estimate Expected Shortfall When Probabilities Are Known With Interval Or Fuzzy Uncertainty, Christian Servin, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

To gauge the risk corresponding to a possible disaster, it is important to know both the probability of this disaster and the expected damage caused by such potential disaster ("expected shortfall"). Both these measures of risk are easy to estimate in the ideal case, when we know the exact probabilities of different disaster strengths. In practice, however, we usually only have a partial information about these probabilities: we may have an interval (or, more generally, fuzzy) uncertainty about these probabilities. In this paper, we show how to efficiently estimate the expected shortfall under such interval and/or fuzzy uncertainty.


Coming Up With A Good Question Is Not Easy: A Proof, Joe Lorkowski, Luc Longpre, Olga Kosheleva, Salem Benferhat Mar 2015

Coming Up With A Good Question Is Not Easy: A Proof, Joe Lorkowski, Luc Longpre, Olga Kosheleva, Salem Benferhat

Departmental Technical Reports (CS)

Ability to ask good questions is an important part of learning skills. Coming up with a good question, a question that can really improve one's understanding of the topic, is not easy. In this paper, we prove -- on the example of probabilistic and fuzzy uncertainty -- that the problem of selecting of a good question is indeed hard.


From 1-D To 2-D Fuzzy: A Proof That Interval-Valued And Complex-Valued Are The Only Distributive Options, Christian Servin, Vladik Kreinovich, Olga Kosheleva Mar 2015

From 1-D To 2-D Fuzzy: A Proof That Interval-Valued And Complex-Valued Are The Only Distributive Options, Christian Servin, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

While the usual 1-D fuzzy logic has many successful applications, in some practical cases, it is desirable to come up with a more subtle way of representing expert uncertainty. A natural idea is to add additional information, i.e., to go from 1-D to 2-D (and multi-D) fuzzy logic. At present, there are two main approaches to 2-D fuzzy logic: interval-valued and complex-valued. At first glance, it may seem that many other options are potentially possible. We show, however, that, under certain reasonable conditions, interval-valued and complex-valued are the only two possible options.


Why It Is Important To Precisiate Goals, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen Mar 2015

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.


Setting Up A Highly Configurable, Scalable Nimbus Cloud Test Bed Running On A Manet, Joshua Mckee Mar 2015

Setting Up A Highly Configurable, Scalable Nimbus Cloud Test Bed Running On A Manet, Joshua Mckee

Departmental Technical Reports (CS)

No abstract provided.


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 Mar 2015

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.


Adding Possibilistic Knowledge To Probabilities Makes Many Problems Algorithmically Decidable, Olga Kosheleva, Vladik Kreinovich Mar 2015

Adding Possibilistic Knowledge To Probabilities Makes Many Problems Algorithmically Decidable, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many physical theories accurately predict which events are possible and which are not, or -- in situations where probabilistic (e.g., quantum) effects are important -- predict the probabilities of different possible outcomes. At first glance, it may seem that this probabilistic information is all we need. We show, however, that to adequately describe physicists' reasoning, it is important to also take into account additional knowledge -- about what is possible and what is not. We show that this knowledge can be described in terms of possibility theory, and that the presence of this knowledge makes many problems algorithmically decidable.


Our Reasoning Is Clearly Fuzzy, So Why Is Crisp Logic So Often Adequate?, Hung T. Nguyen, Berlin Wu, Vladik Kreinovich Feb 2015

Our Reasoning Is Clearly Fuzzy, So Why Is Crisp Logic So Often Adequate?, Hung T. Nguyen, Berlin Wu, Vladik Kreinovich

Departmental Technical Reports (CS)

Our reasoning is clearly fuzzy, so why is crisp logic so often adequate? We explain this phenomenon by showing that in the presence of noise, an arbitrary continuous (e.g., fuzzy) system can be well described by its discrete analog. However, as the description gets more accurate, the continuous description becomes necessary.


A Natural Simple Model Of Scientists' Strength Leads To Skew-Normal Distribution, Komsan Suriya, Tatcha Sudtasan, Tonghui Wang, Octavio Lerma, Vladik Kreinovich Feb 2015

A Natural Simple Model Of Scientists' Strength Leads To Skew-Normal Distribution, Komsan Suriya, Tatcha Sudtasan, Tonghui Wang, Octavio Lerma, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have probability distributions which are close to normal but skewed. Several families of distributions were proposed to describe such phenomena. The most widely used is skew-normal distribution, whose probability density (pdf) is equal to the product of the pdf of a normal distribution and a cumulative distribution function (cdf) of another normal distribution. Out of other possible generalizations of normal distributions, the skew-normal ones were selected because of their computational efficiency, and not because they represent any real-life phenomena. Interestingly, it turns out that these distributions do represent a real-life phenomena: namely, in a natural ...


Fuzzy (And Interval) Techniques In The Age Of Big Data: An Overview With Applications To Environmental Science, Geosciences, Engineering, And Medicine, Vladik Kreinovich, Rujira Ouncharoen Jan 2015

Fuzzy (And Interval) Techniques In The Age Of Big Data: An Overview With Applications To Environmental Science, Geosciences, Engineering, And Medicine, Vladik Kreinovich, Rujira Ouncharoen

Departmental Technical Reports (CS)

In some practical situations -- e.g., when treating a new illness -- we do not have enough data to make valid statistical conclusions. In such situations, it is necessary to use expert knowledge -- and thus, it is beneficial to use fuzzy techniques that were specifically designed to process such knowledge. At first glance, it may seem that in situations when we have large amounts of data, the relative importance of expert knowledge should decrease. However, somewhat surprisingly, it turns out that expert knowledge is still very useful in the current age of big data. In this paper, we explain how exactly ...


Wiener-Process-Type Evasive Aircraft Actions Are Indeed Optimal Against Anti-Aircraft Guns: Wiener's Data Revisited, Vladik Kreinovich, Olga Kosheleva Jan 2015

Wiener-Process-Type Evasive Aircraft Actions Are Indeed Optimal Against Anti-Aircraft Guns: Wiener's Data Revisited, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In his 1940s empirical study of evasive aircraft actions, N.~Wiener, the father of cybernetics, founds out that the pilot's actions follow a Wiener-type-process. In this paper, we explain this empirical result by showing that such evasive actions are indeed optimal against the 1940s anti-aircraft guns.


Testing A Power Law Model Of Knowledge Propagation: Case Study Of The Out Of Eden Walk Project, Octavio Lerma, Leobardo Valera, Deana Pennington, Vladik Kreinovich Jan 2015

Testing A Power Law Model Of Knowledge Propagation: Case Study Of The Out Of Eden Walk Project, Octavio Lerma, Leobardo Valera, Deana Pennington, Vladik Kreinovich

Departmental Technical Reports (CS)

To improve teaching and learning, it is important to understand how knowledge propagates. In general, when a new piece of knowledge is introduced, people start learning about it. Since the potential audience is limited, after some time, the number of new learners starts to decrease. Traditional models of knowledge propagation are based on differential equations; in these models, the number of new learners decreases exponentially with time. Recently, a new power law model for knowledge propagation was proposed. In this model, the number of learners decreases much slower, as a negative power of time. In this paper, we compare the ...


Optimizing Pred(25) Is Np-Hard, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich Jan 2015

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 ...


Towards The Possibility Of Objective Interval Uncertainty In Physics. Ii, Luc Longpre, Olga Kosheleva, Vladik Kreinovich Jan 2015

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 relativity ...


How Design Quality Improves With Increasing Computational Abilities: General Formulas And Case Study Of Aircraft Fuel Efficiency, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich, Sergei Soloviev Jan 2015

How Design Quality Improves With Increasing Computational Abilities: General Formulas And Case Study Of Aircraft Fuel Efficiency, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich, Sergei Soloviev

Departmental Technical Reports (CS)

It is known that the problems of optimal design are NP-hard -- meaning that, in general, a feasible algorithm can only produce close-to-optimal designs. The more computations we perform, the better design we can produce. In this paper, we theoretically derive quantitative formulas describing how the design qualities improves with the increasing computational abilities. We then empirically confirm the resulting theoretical formula by applying it to the problem of aircraft fuel efficiency.


Constraint Approach To Multi-Objective Optimization, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich Jan 2015

Constraint Approach To Multi-Objective Optimization, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we would like to maximize (or minimize) several different criteria, and it is not clear how much weight to assign to each of these criteria. Such situations are ubiquitous and thus, it is important to be able to solve the corresponding multi-objective optimization problems. There exist many heuristic methods for solving such problems. In this paper, we reformulate multi-objective optimization as a constraint satisfaction problem, and we show that this reformulation explains two widely use multi-objective optimization techniques: optimizing a weighted sum of the objective functions and optimizing the product of normalized values of these functions.


Minimax Portfolio Optimization Under Interval Uncertainty, Meng Yuan, Xu Lin, Junzo Watada, Vladik Kreinovich Jan 2015

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 ...


Need For Data Processing Naturally Leads To Fuzzy Logic (And Neural Networks): Fuzzy Beyond Experts And Beyond Probabilities, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta Dec 2014

Need For Data Processing Naturally Leads To Fuzzy Logic (And Neural Networks): Fuzzy Beyond Experts And Beyond Probabilities, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

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 ...


Every Sue Function Is A Ratio Of Two Multi-Linear Functions, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich Dec 2014

Every Sue Function Is A Ratio Of Two Multi-Linear Functions, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

We prove that the function computed by each single-use expression is a ratio of two multi-linear functions.


When Can We Reduce Multi-Variable Range Estimation Problem To Two Fewer-Variable Problems?, Joe Lorkowski, Olga Kosheleva, Luc Longpre, Vladik Kreinovich Dec 2014

When Can We Reduce Multi-Variable Range Estimation Problem To Two Fewer-Variable Problems?, Joe Lorkowski, Olga Kosheleva, Luc Longpre, Vladik Kreinovich

Departmental Technical Reports (CS)

Sometimes, a function f of n variables can be represented as a composition of two functions of fewer variables. In this case, the problem of computing the range of f on given intervals can be reduced to two range-computation problems with fewer variables. In this paper, we describe a feasible algorithm that checks whether such a reduction is possible -- and, if it is possible, produces the desired reduction.