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Articles 1 - 22 of 22
Full-Text Articles in Physical Sciences and Mathematics
F-Transform In View Of Trend Extraction, Irina Perfilieva, Vladik Kreinovich, Vilém Novák
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.
Metrological Self-Assurance Of Data Processing Software, Vladik Kreinovich, Leonid Reznik, Konstantin K. Semenov, Gennady N. Solopchenko
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.
Thirty-Two Sample Audio Search Tasks, Nigel G. Ward, Steven D. Werner
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.
Zadeh's Vision Of Going From Fuzzy To Computing With Words: From The Idea's Origin To Current Successes To Remaining Challenges, Vladik Kreinovich
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.
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
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 …
Interval Uncertainty As The Basis For A General Description Of Uncertainty: A Position Paper, Vladik Kreinovich
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. …
Kansei Engineering: Towards Optimal Set Of Designs, Van-Nam Huynh, Octavio Lerma, Vladik Kreinovich
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.
Orders On Intervals Over Partially Ordered Sets: Extending Allen's Algebra And Interval Graph Results, Francisco Zapata, Vladik Kreinovich, Cliff Joslyn, Emilie Hogan
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 …
How To Define Mean, Variance, Etc., For Heavy-Tailed Distributions: A Fractal-Motivated Approach, Vladik Kreinovich, Olga Kosheleva
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.
Interval Or Moments: Which Carry More Information?, Michael Beer, Vladik Kreinovich
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 …
How To Divide Students Into Groups So As To Optimize Learning: Towards A Solution To A Pedagogy-Related Optimization Problem, Olga Kosheleva, Vladik Kreinovich
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.
Decision Making Under Interval And Fuzzy Uncertainty: Towards An Operational Approach, Rafik Aliev, Oleg H. Huseynov, Vladik Kreinovich
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. …
Membership Functions Or Alpha-Cuts? Algorithmic (Constructivist) Analysis Justifies An Interval Approach, Vladik Kreinovich
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.
An Evaluation Approach For Interactions Between Abstract Workflows And Provenance Traces, Leonardo Salayandia, Ann Q. Gates, Paulo Pinheiro
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 …
Estimating Correlation Under Interval And Fuzzy Uncertainty: Case Of Hierarchical Estimation, Ali Jalal-Kamali
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 …
Semi-Heuristic Target-Based Fuzzy Decision Procedures: Towards A New Interval Justification, Christian Servin, Van-Nam Huynh, Yoshiteru Nakamori
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
Extending Java For Android Programming, Yoonsik Cheon
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.
Modal Intervals As A New Logical Interpretation Of The Usual Lattice Order Between Interval Truth Values, Francisco Zapata
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. …
Image And Model Fusion: Unexpected Counterintuitive Behavior Of Traditional Statistical Techniques And Resulting Need For Expert Knowledge, Omar Ochoa, Aaron A. Velasco, Vladik Kreinovich
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 …
Simplicity Is Worse Than Theft: A Constraint-Based Explanation Of A Seemingly Counter-Intuitive Russian Saying, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Simplicity Is Worse Than Theft: A Constraint-Based Explanation Of A Seemingly Counter-Intuitive Russian Saying, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, simplified models, models that enable us to gauge the quality of different decisions reasonably well, lead to far-from-optimal situations when used in searching for an optimal decision. There is even an appropriate Russian saying: simplicity is worse than theft. In this paper, we provide a mathematical explanation of this phenomenon.
Kinematic Spaces And De Vries Algebras: Towards Possible Physical Meaning Of De Vries Algebras, Olga Kosheleva, Francisco Zapata
Kinematic Spaces And De Vries Algebras: Towards Possible Physical Meaning Of De Vries Algebras, Olga Kosheleva, Francisco Zapata
Departmental Technical Reports (CS)
Traditionally, in physics, space-times are described by (pseudo-)Riemann spaces, i.e., by smooth manifolds with a tensor metric field. However, in several physically interesting situations smoothness is violated: near the Big Bang, at the black holes, and on the microlevel, when we take into account quantum effects. In all these situations, what remains is causality -- an ordering relation. To describe such situations, in the 1960s, geometers H. Busemann and R. Pimenov and physicists E. Kronheimer and R. Penrose developed a theory of kinematic spaces. Originally, kinematic spaces were formulated as topological ordered spaces, but it turned out that kinematic …
Algorithmics Of Checking Whether A Mapping Is Injective, Surjective, And/Or Bijective, E. Cabral Balreira, Olga Kosheleva, Vladik Kreinovich
Algorithmics Of Checking Whether A Mapping Is Injective, Surjective, And/Or Bijective, E. Cabral Balreira, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many situations, we would like to check whether an algorithmically given mapping f:A --> B is injective, surjective, and/or bijective. These properties have a practical meaning: injectivity means that the events of the action f can be, in principle, reversed, while surjectivity means that every state b from the set B can appear as a result of the corresponding action. In this paper, we discuss when algorithms are possible for checking these properties.