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Departmental Technical Reports (CS)

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Full-Text Articles in Computer Sciences

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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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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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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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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Simplicity Is Worse Than Theft: A Constraint-Based Explanation Of A Seemingly Counter-Intuitive Russian Saying, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich Apr 2012

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.

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Algorithmics Of Checking Whether A Mapping Is Injective, Surjective, And/Or Bijective, E. Cabral Balreira, Olga Kosheleva, Vladik Kreinovich Apr 2012

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.

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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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Kinematic Spaces And De Vries Algebras: Towards Possible Physical Meaning Of De Vries Algebras, Olga Kosheleva, Francisco Zapata Apr 2012

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 …

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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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Estimating Sample Mean Under Interval Uncertainty And Constraint On Sample Varience, Misha Koshelev, Ali Jalal-Kamali, Luc Longpre Jan 2011

Estimating Sample Mean Under Interval Uncertainty And Constraint On Sample Varience, Misha Koshelev, Ali Jalal-Kamali, Luc Longpre

Departmental Technical Reports (CS)

Traditionally, practitioners start a statistical analysis of a given sample x1, … , xn by computing the sample mean E and the sample variance V. The sample values xi usually come from measurements. Measurements are never absolutely accurate and often, the only information that we have about the corresponding measurement errors are the upper bounds Δi on these errors. In such situations, after obtaining the measurement result , the only information that we have about the actual (unknown) value xi of the ith quantity is that xi belongs to the interval …

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How To Reconstruct The System's Dynamics By Differentiating Interval-Valued And Set-Valued Functions, Karen Villaverde, Olga Kosheleva Jan 2011

How To Reconstruct The System's Dynamics By Differentiating Interval-Valued And Set-Valued Functions, Karen Villaverde, Olga Kosheleva

Departmental Technical Reports (CS)

To predict the future state of a physical system, we must know the differential equations x = f(x) that describe how this state changes with time. In many practical situations, we can observe individ­ual trajectories x(t). By differentiating these trajectories with respect to time, we can determine the values of f(x) for different states x; if we observe many such trajectories, we can reconstruct the function f( x). However, in many other cases, we do not observe individual systems, we observe a set X of such systems. We can observe how this set X changes, but not how individual …

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