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2012

University of Texas at El Paso

Articles 1 - 30 of 122

Full-Text Articles in Physical Sciences and Mathematics

Decision Making Under Interval Uncertainty (And Beyond), Vladik Kreinovich Dec 2012

Decision Making Under Interval Uncertainty (And Beyond), Vladik Kreinovich

Departmental Technical Reports (CS)

To make a decision, we must find out the user's preference, and help the user select an alternative which is the best -- according to these preferences. Traditional utility-based decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is often unable to select one of these alternatives. In this chapter, we show how we can extend the utility-based decision theory to such realistic (interval) cases.

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F-Transform In View Of Trend Extraction, Irina Perfilieva, Vladik Kreinovich, Vilém Novák Dec 2012

F-Transform In View Of Trend Extraction, Irina Perfilieva, Vladik Kreinovich, Vilém Novák

Departmental Technical Reports (CS)

In the analysis of time series, it is important to decompose the original values into trend, cycle, seasonal component, and noise. In this paper, we provide a theoretical justification of the fact that the F-transform can be used for this purpose. We formulate "natural" requirements on the trend extraction procedure and then show that the inverse F-transform fulfils all of them.

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Metrological Self-Assurance Of Data Processing Software, Vladik Kreinovich, Leonid Reznik, Konstantin K. Semenov, Gennady N. Solopchenko Dec 2012

Metrological Self-Assurance Of Data Processing Software, Vladik Kreinovich, Leonid Reznik, Konstantin K. Semenov, Gennady N. Solopchenko

Departmental Technical Reports (CS)

The metrological self-assurance for data processing software is discussed. The way to achieve this property for software is presented.

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Thirty-Two Sample Audio Search Tasks, Nigel G. Ward, Steven D. Werner Nov 2012

Thirty-Two Sample Audio Search Tasks, Nigel G. Ward, Steven D. Werner

Departmental Technical Reports (CS)

Searching in audio archives is potentially very useful, and good evaluations can guide development to realize that promise. However most current evaluation programs are technology-centric, rather than user-oriented and task-centric. This paper examines current and potential audio search needs and scenarios, and presents a sample set of thirty-two diverse audio search tasks to support more realistic evaluations.

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Should Voting Be Mandatory? Democratic Decision Making From The Economic Viewpoint, Olga Kosheleva, Vladik Kreinovich, Boakun Li Nov 2012

Should Voting Be Mandatory? Democratic Decision Making From The Economic Viewpoint, Olga Kosheleva, Vladik Kreinovich, Boakun Li

Departmental Technical Reports (CS)

Many decisions are made by voting. At first glance, the more people participate in the voting process, the more democratic -- and hence, better -- the decision. In this spirit, to encourage everyone's participation, several countries make voting mandatory. But does mandatory voting really make decisions better for the society? In this paper, we show that from the viewpoint of decision making theory, it is better to allow undecided voters not to participate in the voting process. We also show that the voting process would be even better -- for the society as a whole -- if we allow partial …

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Zadeh's Vision Of Going From Fuzzy To Computing With Words: From The Idea's Origin To Current Successes To Remaining Challenges, Vladik Kreinovich Nov 2012

Zadeh's Vision Of Going From Fuzzy To Computing With Words: From The Idea's Origin To Current Successes To Remaining Challenges, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

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Ubiquity Of Data And Model Fusion: From Geophysics And Environmental Sciences To Estimating Individual Risk During An Epidemic, Omar Ochoa, Aline Jaimes, Christian Servin, Craig Tweedie, Aaron Velasco, Martine Ceberio, Vladik Kreinovich Nov 2012

Ubiquity Of Data And Model Fusion: From Geophysics And Environmental Sciences To Estimating Individual Risk During An Epidemic, Omar Ochoa, Aline Jaimes, Christian Servin, Craig Tweedie, Aaron Velasco, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to combine the results of measuring a local value of a certain quantity with results of measuring average values of this same quantity. For example, in geosciences, we need to combine the seismic models (which describe density at different locations and depths) with gravity models which describe density averaged over certain regions. Similarly, in estimating the risk of an epidemic to an individual, we need to combine probabilities describe the risk to people of the corresponding age group, to people of the corresponding geographical region, etc. In this paper, we provide general techniques for …

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How To Define Relative Approximation Error Of An Interval Estimate: A Proposal, Vladik Kreinovich Oct 2012

How To Define Relative Approximation Error Of An Interval Estimate: A Proposal, Vladik Kreinovich

Departmental Technical Reports (CS)

The traditional definition of a relative approximation error of an estimate X as the ratio |X - x|/|x| does not work when the actual value x is 0. To avoid this problem, we propose a new definition |X - x|/|X|. We show how this definition can be naturally extended to the case when instead of a numerical estimate X, we have an interval estimate [x], i.e., an interval that is guaranteed to contain the actual (unknown) value x.

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Interval Uncertainty As The Basis For A General Description Of Uncertainty: A Position Paper, Vladik Kreinovich Oct 2012

Interval Uncertainty As The Basis For A General Description Of Uncertainty: A Position Paper, Vladik Kreinovich

Departmental Technical Reports (CS)

Uncertainty is ubiquitous. Depending on what information we have, we get different types of uncertainty. For each type of uncertainty, techniques have been developed for efficient representation and processing of this uncertainty. However, the plethora of different uncertainty techniques is often confusing for practitioners. The situation is especially difficult in frequent situations when we need to gauge the uncertainty of the result of complex multi-stage data processing, and different data inputs are known with different types of uncertainty. To avoid this problem, it is necessary to develop and implement a general approach to representing and processing different types of uncertainty. …

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Why Clayton And Gumbel Copulas: A Symmetry-Based Explanation, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta Sep 2012

Why Clayton And Gumbel Copulas: A Symmetry-Based Explanation, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

In econometrics, many distributions are non-Gaussian. To describe dependence between non-Gaussian variables, it is usually not sufficient to provide their correlation: it is desirable to also know the corresponding copula. There are many different families of copulas; which family shall we use? In many econometric applications, two families of copulas have been most efficient: the Clayton and the Gumbel copulas. In this paper, we provide a theoretical explanation for this empirical efficiency, by showing that these copulas naturally follow from reasonable symmetry assumptions. This symmetry justification also allows us to provide recommendations about which families of copulas we should use …

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If Energy Is Not Preserved, Then Planck's Constant Is No Longer A Constant: A Theorem, Vladik Kreinovich, Andres Ortiz Sep 2012

If Energy Is Not Preserved, Then Planck's Constant Is No Longer A Constant: A Theorem, Vladik Kreinovich, Andres Ortiz

Departmental Technical Reports (CS)

For any physical theory, to experimentally check its validity, we need to formulate an alternative theory and check whether the experimental results are consistent with the original theory or with an alternative theory. In particular, to check whether energy is preserved, it is necessary to formulate an alternative theory in which energy is not preserved. Formulating such a theory is not an easy task in quantum physics, where the usual Schroedinger equation implicitly assumes the existence of an energy (Hamiltonian) operator whose value is preserved. In this paper, we show that the only way to get a consistent quantum theory …

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Towards Unique Physically Meaningful Definitions Of Random And Typical Objects, Luc Longpre, Olga Kosheleva Sep 2012

Towards Unique Physically Meaningful Definitions Of Random And Typical Objects, Luc Longpre, Olga Kosheleva

Departmental Technical Reports (CS)

To distinguish between random and non-random sequence, Kolmogorov and Martin-Lof proposed a new definition of randomness, according to which an object (e.g., a sequence of 0s and 1s) if random if it satisfies all probability laws, i.e., in more precise terms, if it does not belong to any definable set of probability measure 0. This definition reflect the usual physicists' idea that events with probability 0 cannot happen. Physicists -- especially in statistical physics -- often claim a stronger statement: that events with a very small probability cannot happen either. A modification of Kolmogorov-Martin-Lof's (KLM) definition has been proposed to …

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In Applications, A Rigorous Proof Is Not Enough: It Is Also Important To Have An Intuitive Understanding, Vladik Kreinovich Aug 2012

In Applications, A Rigorous Proof Is Not Enough: It Is Also Important To Have An Intuitive Understanding, Vladik Kreinovich

Departmental Technical Reports (CS)

From a purely mathematical viewpoint, once a statement is rigorously proven, it should be accepted as true. Surprisingly, in applications, users are often reluctant to accept a rigorously proven statement until the proof is supplemented by its intuitive explanation. In this paper, we show that this seemingly unreasonable reluctance makes perfect sense: the proven statement is about the mathematical model which is an approximation to the actual system; an intuitive explanation provides some confidence that the statement holds not only for the model, but also for systems approximately equal to this model -- in particular, for the actual system of …

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In Quantum Physics, Free Will Leads To Nonconservation Of Energy, Vladik Kreinovich Aug 2012

In Quantum Physics, Free Will Leads To Nonconservation Of Energy, Vladik Kreinovich

Departmental Technical Reports (CS)

Modern physical theories are deterministic in the sense that once we know the current state of the world, we can, in principle, predict all the future states. This was true for classical (pre-quantum) theories, this is true for modern quantum physics. On the other hand, we all know that we can make decision that change the state of the world -- even if, for most of us, a little bit. This intuitive idea of free will permeates all our life, all our activities -- and it seems to contradict the determinism of modern physics. It is therefore desirable to incorporate …

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Kansei Engineering: Towards Optimal Set Of Designs, Van-Nam Huynh, Octavio Lerma, Vladik Kreinovich Aug 2012

Kansei Engineering: Towards Optimal Set Of Designs, Van-Nam Huynh, Octavio Lerma, Vladik Kreinovich

Departmental Technical Reports (CS)

In many engineering situations, we need to take into account subjective user preferences; taking such preference into account is known as {\em Kansei Engineering}. In this paper, we formulate the problem of selecting optimal set of designs in Kansei engineering as a mathematical optimization problem, and we provide an explicit solution to this optimization problem.

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Possible And Necessary Orders, Equivalences, Etc.: From Modal Logic To Modal Mathematics, Francisco Zapata, Olga Kosheleva Aug 2012

Possible And Necessary Orders, Equivalences, Etc.: From Modal Logic To Modal Mathematics, Francisco Zapata, Olga Kosheleva

Departmental Technical Reports (CS)

In practice, we are often interested in order relations (e.g., when we describe preferences) or equivalence relations (e.g., when we describe clustering). Often, we do not have a complete information about the corresponding relation; as a result, we have several relations consistent with our knowledge. In such situations, it is desirable to know which elements a and b are possibly connected by the relation and which are necessarily connected by this relation. In this paper, we provide a full description of all such possible and necessary orders and equivalence relations. For example, possible orders are exactly reflexive relations, while necessary …

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Orders On Intervals Over Partially Ordered Sets: Extending Allen's Algebra And Interval Graph Results, Francisco Zapata, Vladik Kreinovich, Cliff Joslyn, Emilie Hogan Aug 2012

Orders On Intervals Over Partially Ordered Sets: Extending Allen's Algebra And Interval Graph Results, Francisco Zapata, Vladik Kreinovich, Cliff Joslyn, Emilie Hogan

Departmental Technical Reports (CS)

To make a decision, we need to compare the values of quantities. In many practical situations, we know the values with interval uncertainty. In such situations, we need to compare intervals. Allen's algebra describes all possible relations between intervals on the real line which are generated by the ordering of endpoints; ordering relations between such intervals have also been well studied. In this paper, we extend this description to intervals in an arbitrary partially ordered set (poset). In particular, we explicitly describe ordering relations between intervals that generalize relation between points. As auxiliary results, we provide a logical interpretation of …

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How To Define Mean, Variance, Etc., For Heavy-Tailed Distributions: A Fractal-Motivated Approach, Vladik Kreinovich, Olga Kosheleva Aug 2012

How To Define Mean, Variance, Etc., For Heavy-Tailed Distributions: A Fractal-Motivated Approach, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical situations, we encounter heavy-tailed distributions for which the variance -- and even sometimes the mean -- are infinite. We propose a fractal-motivated approach that enables us to gauge the mean and variance of such distributions.

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From Unbiased Numerical Estimates To Unbiased Interval Estimates, Baokun Li, Gang Xiang, Vladik Kreinovich, Panagios Moscopoulos Aug 2012

From Unbiased Numerical Estimates To Unbiased Interval Estimates, Baokun Li, Gang Xiang, Vladik Kreinovich, Panagios Moscopoulos

Departmental Technical Reports (CS)

One of the main objectives of statistics is to estimate the parameters of a probability distribution based on a sample taken from this distribution. Of course, since the sample is finite, the estimate X is, in general, different from the actual value x of the corresponding parameter. What we can require is that the corresponding estimate is unbiased, i.e., that the mean value of the difference X - x is equal to 0: E[X] = x. In some problems, unbiased estimates are not possible. We show that in some such problems, it is possible to have interval unbiased estimates, i.e., …

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Interval Or Moments: Which Carry More Information?, Michael Beer, Vladik Kreinovich Jul 2012

Interval Or Moments: Which Carry More Information?, Michael Beer, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we do not have enough observations to uniquely determine the corresponding probability distribution, we only have enough observations to estimate two parameters of this distribution. In such cases, the traditional statistical approach is to estimate the mean and the standard deviation. Alternatively, we can estimate the two bounds that form the range of the corresponding variable and thus, generate an interval. Which of these two approaches should we select? A natural idea is to select the most informative approach, i.e., an approach in which we need the smallest amount of additional information (in Shannon's sense) to …

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How To Divide Students Into Groups So As To Optimize Learning: Towards A Solution To A Pedagogy-Related Optimization Problem, Olga Kosheleva, Vladik Kreinovich Jul 2012

How To Divide Students Into Groups So As To Optimize Learning: Towards A Solution To A Pedagogy-Related Optimization Problem, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To enhance learning, it is desirable to also let students learn from each other, e.g., by working in groups. It is known that such groupwork can improve learning, but the effect strongly depends on how we divide students into groups. In this paper, based on a first approximation model of student interaction, we describe how to optimally divide students into groups so as to optimize the resulting learning. We hope that, by taking into account other aspects of student interaction, it will be possible to transform our solution into truly optimal practical recommendations.

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Decision Making Under Interval And Fuzzy Uncertainty: Towards An Operational Approach, Rafik Aliev, Oleg H. Huseynov, Vladik Kreinovich Jul 2012

Decision Making Under Interval And Fuzzy Uncertainty: Towards An Operational Approach, Rafik Aliev, Oleg H. Huseynov, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is either completely unable to select one of these alternatives, or selects one of the alternatives only "to some extent". How can we extend the traditional decision theory to such realistic interval and fuzzy cases? In their previous papers, the first two authors proposed a natural generalization of the usual decision theory axioms to interval and fuzzy cases, and described decision coming from this generalization. …

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Membership Functions Or Alpha-Cuts? Algorithmic (Constructivist) Analysis Justifies An Interval Approach, Vladik Kreinovich Jul 2012

Membership Functions Or Alpha-Cuts? Algorithmic (Constructivist) Analysis Justifies An Interval Approach, Vladik Kreinovich

Departmental Technical Reports (CS)

In his pioneering papers, Igor Zaslavsky started an algorithmic (constructivist) analysis of fuzzy logic. In this paper, we extend this analysis to fuzzy mathematics and fuzzy data processing. Specifically, we show that the two mathematically equivalent representations of a fuzzy number -- by a membership function and by alpha-cuts -- are not algorithmically equivalent, and only the alpha-cut representation enables us to efficiently process fuzzy data.

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An Evaluation Approach For Interactions Between Abstract Workflows And Provenance Traces, Leonardo Salayandia, Ann Q. Gates, Paulo Pinheiro Jun 2012

An Evaluation Approach For Interactions Between Abstract Workflows And Provenance Traces, Leonardo Salayandia, Ann Q. Gates, Paulo Pinheiro

Departmental Technical Reports (CS)

In the context of science, abstract workflows bridge the gap between scientists and technologists towards using computer systems to carry out scientific processes. Provenance traces provide evidence required to validate scientific products and support their secondary use. Assuming abstract workflows and provenance traces are based on formal semantics, a knowledge-based system that consistently merges both technologies allows scientists to document their processes of data collection and transformation; it also allows for secondary users of data to assess scientific processes and resulting data products. This paper presents an evaluation approach for interactions between abstract workflows and provenance traces. The claim is …

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Estimating Correlation Under Interval And Fuzzy Uncertainty: Case Of Hierarchical Estimation, Ali Jalal-Kamali May 2012

Estimating Correlation Under Interval And Fuzzy Uncertainty: Case Of Hierarchical Estimation, Ali Jalal-Kamali

Departmental Technical Reports (CS)

In many situations, we are interested in finding the correlation ρ between different quantities x and y based on the values xi and yi of these quantities measured in different situations i. The correlation is easy to compute when we know the exact sample values xi and yi. In practice, the sample values come from measurements or from expert estimates; in both cases, the values are not exact. Sometimes, we know the probabilities of different values of measurement errors, but in many cases, we only know the upper bounds Δxi and Δyi on …

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How To Define Average Class Size (And Deviations From The Average Class Size) In A Way Which Is Most Adequate For Teaching Effectiveness, Olga Kosheleva, Vladik Kreinovich May 2012

How To Define Average Class Size (And Deviations From The Average Class Size) In A Way Which Is Most Adequate For Teaching Effectiveness, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When students select a university, one of the important parameters is the average class size. This average is usually estimated as an arithmetic average of all the class sizes. However, it has been recently shown that to more adequately describe students' perception of a class size, it makes more sense to average not over classes, but over all students -- which leads to a different characteristics of the average class size. In this paper, we analyze which characteristic is most adequate from the viewpoint of efficient learning. Somewhat surprisingly, it turns out that the arithmetic average is the most adequate …

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Semi-Heuristic Target-Based Fuzzy Decision Procedures: Towards A New Interval Justification, Christian Servin, Van-Nam Huynh, Yoshiteru Nakamori May 2012

Semi-Heuristic Target-Based Fuzzy Decision Procedures: Towards A New Interval Justification, Christian Servin, Van-Nam Huynh, Yoshiteru Nakamori

Departmental Technical Reports (CS)

To more adequately describe human decision making, V.-N. Nuynh, Y. Nakamori, and others proposed a special semi-heuristic target-based fuzzy decision procedure. A usual justification for this procedure is based on the selection of the simplest possible membership functions and "and"- and "or"-operations; if we use more complex membership functions and "and"- and "or"-operations, we get different results. Interestingly, in practical applications, the procedure based on the simplest choices most adequately describes human preferences. It is therefore desirable to come up with a justification that explains this empirical fact. Such a justification is proposed in this paper

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Extending Java For Android Programming, Yoonsik Cheon Apr 2012

Extending Java For Android Programming, Yoonsik Cheon

Departmental Technical Reports (CS)

Android is one of the most popular platforms for developing mobile applications. However, its framework relies on programming conventions and styles to implement framework-specific concepts like activities and intents, causing problems such as reliability, readability, understandability, and maintainability. We propose to extend Java to support Android framework concepts explicitly as built-in language features. Our extension called Android Java will allow Android programmers to express these concepts in a more reliable, natural, and succinct way.

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Modal Intervals As A New Logical Interpretation Of The Usual Lattice Order Between Interval Truth Values, Francisco Zapata Apr 2012

Modal Intervals As A New Logical Interpretation Of The Usual Lattice Order Between Interval Truth Values, Francisco Zapata

Departmental Technical Reports (CS)

In the traditional fuzzy logic, we use numbers from the interval [0,1] to describe possible expert's degrees of belief in different statements. Comparing the resulting numbers is straightforward: if our degree of belief in a statement A is larger than our degree of belief in a statement B, this means that we have more confidence in the statement $A$ than in the statement B. It is known that to get a more adequate description of the expert's degree of belief, it is better to use not only numbers $a$ from the interval [0,1], but also subintervals [a1,a2] of this interval. …

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Image And Model Fusion: Unexpected Counterintuitive Behavior Of Traditional Statistical Techniques And Resulting Need For Expert Knowledge, Omar Ochoa, Aaron A. Velasco, Vladik Kreinovich Apr 2012

Image And Model Fusion: Unexpected Counterintuitive Behavior Of Traditional Statistical Techniques And Resulting Need For Expert Knowledge, Omar Ochoa, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, we have different types of data. For example, in geosciences, we have seismic data, gravity data, magnetic data, etc. Ideally, we should jointly process all this data, but often, such a joint processing is not yet practically possible. In such situations, it is desirable to "fuse" models (images) corresponding to different types of data: e.g., to fuse an image corresponding to seismic data and an image corresponding to gravity data. At first glance, if we assume that all the approximation errors are independent and normally distributed, then we get a reasonably standard statistical problem which can …

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