Computer Sciences Commons^™

A Possible Utility-Based Explanation Of Deaton's Paradox (And Habits Of Mind), Hung T. Nguyen, Songsak Sriboonchitta, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Towards Making Theory Of Computation Course More Understandable And Relevant: Recursive Functions, For-Loops, And While-Loops, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In this paper, we show how we can make a theory of computation course more understandable and more relevant: namely, we show that a seemingly abstract notion of primitive recursion is a direct counterpart to for-loops, while the mu-recursion is an analog of while-loops.

How To Compute Von Neumann-Morgenstern Solutions, Martha Osegueda Escobar, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

How To Modify Data Processing Algorithms So That They Detect Only Dependencies Which Make Sense To Domain Experts, Geovany Ramirez, Craig Tweedie, Jason Carlsson, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

How To Divide A Territory: An Argument In Favor Of Private Property, Mahdokhat Afravi, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Combining Interval And Probabilistic Uncertainty: What Is Computable?, Vladik Kreinovich, Andrzej Pownuk, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical problems, we need to process measurement results. For example, we need such data processing to predict future values of physical quantities. In these computations, it is important to take into account that measurement results are never absolutely exact, that there is always measurement uncertainty, because of which the measurement results are, in general, somewhat different from the actual (unknown) values of the corresponding quantities. In some cases, all we know about measurement uncertainty is an upper bound; in this case, we have an interval uncertainty, meaning that all we know about the actual value is that is …

Why Linear (And Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic And Financial Phenomena: A Fuzzy-Based Explanation, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Economic and financial phenomena are highly complex and non-linear. However, surprisingly, in many cases, these phenomena are accurately described by linear models -- or, sometimes, by piecewise linear ones. In this paper, we show that fuzzy techniques can explain the unexpected efficiency of linear and piecewise linear models: namely, we show that a natural fuzzy-based precisiation of imprecise ("fuzzy") expert knowledge often leads to linear and piecewise linear models.

We also discuss which expert-motivated nonlinear models should be used to get a more accurate description of economic and financial phenomena.

When Should We Switch From Interval-Valued Fuzzy To Full Type-2 Fuzzy (E.G., Gaussian)?, Vladik Kreinovich, Chrysostomos D. Stylios

Departmental Technical Reports (CS)

Full type-2 fuzzy techniques provide a more adequate representation of expert knowledge. However, such techniques also require additional computational efforts, so we should only use them if we expect a reasonable improvement in the result of the corresponding data processing. It is therefore important to come up with a practically useful criterion for deciding when we should stay with interval-valued fuzzy and when we should use full type-2 fuzzy techniques. Such a criterion is proposed in this paper. We also analyze how many experts we need to ask to come up with a reasonable description of expert uncertainty.

Student Autonomy Improves Learning: A Theoretical Justification Of The Empirical Results, Octavio Lerma, Vladik Kreinovich

Departmental Technical Reports (CS)

In many pedagogical situations, it is advantageous to give students some autonomy: for example, instead of assigning the same homework problem to all the students, to give students a choice between several similar problems, so that each student can choose a problem whose context best fits his or her experiences. A recent experimental study shows that there is a 45% correlation between degree of autonomy and student success. In this paper, we provide a theoretical explanation for this correlation value.

Why Deep Neural Networks: A Possible Theoretical Explanation, Chitta Baral, Olac Fuentes, Vladik Kreinovich

Departmental Technical Reports (CS)

In the past, the most widely used neural networks were 3-layer ones. These networks were preferred, since one of the main advantages of the biological neural networks -- which motivated the use of neural networks in computing -- is their parallelism, and 3-layer networks provide the largest degree of parallelism. Recently, however, it was empirically shown that, in spite of this argument, multi-layer ("deep") neural networks leads to a much more efficient machine learning. In this paper, we provide a possible theoretical explanation for the somewhat surprising empirical success of deep networks.

Dow Theory's Peak-And-Trough Analysis Justified, Chrysostomos Stylios, Vladik Kreinovich

Departmental Technical Reports (CS)

In the analysis of dynamic financial quantities such as stock prices, equity prices, etc., reasonable results are often obtained if we only consider local maxima ("peaks") and local minima ("troughs") and ignore all the other values. The empirical success of this strategy remains a mystery. In this paper, we provide a possible explanation for this success.

How To Gauge Disruptions Caused By Garbage Collection: Towards An Efficient Algorithm, Gabriel Arellano, Edward Hudgins, David Pruitt, Adrian Veliz, Eric Freudenthal, Vladik Kreinovich

Departmental Technical Reports (CS)

Comprehensive garbage collection is employed on a variety of computing devices, including intelligent cell phones. Garbage collection can cause prolonged user-interface pauses. In order to evaluate and compare the disruptiveness of various garbage collection strategies, it is necessary to gauge disruptions caused by garbage collection. In this paper, we describe efficient algorithms for computing metrics useful for this purpose.

How To Take Into Account A Student's Degree Of Certainty When Evaluating The Test Results, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To more adequately gauge the student's knowledge, it is desirable to take into account not only whether the student's answers on the test are correct or nor, but also how confident the students are in their answers. For example, a situation when a student gives a wrong answer, but understands his/her lack of knowledge on this topic, is not as harmful as the situation when the student is absolutely confident in his/her wrong answer. In this paper, we use the general decision making theory to describe the best way to take into account the student's degree of certainty when evaluating …

In Engineering Classes, How To Assign Partial Credit: From Current Subjective Practice To Exact Formulas (Based On Computational Intelligence Ideas), Joe Lorkowski, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

When a student performed only some of the steps needed to solve a problem, this student gets partial credit. This partial credit is usually proportional to the number of stages that the student performed. This may sound reasonable, but in engineering education, this leads to undesired consequences: for example, a student who did not solve any of the 10 problems on the test, but who successfully performed 9 out of 10 stages needed to solve each problem will still get the grade of A ("excellent"). This may be a good evaluation of the student's intellectual ability, but for a engineering …

Why Fuzzy Cognitive Maps Are Efficient, Vladik Kreinovich, Chrysostomos Stylios

Departmental Technical Reports (CS)

In many practical situations, the relation between the experts' degrees of confidence in different related statements is well described by Fuzzy Cognitive Maps (FCM). This empirical success is somewhat puzzling, since from the mathematical viewpoint, each FCM relation corresponds to a simplified one-neuron neural network, and it is well known that to adequately describe relations, we need multiple neurons. In this paper, we show that the empirical success of FCM can be explained if we take into account that human's subjective opinions follow Miller's seven plus minus two law.

Analysis Of Random Metric Spaces Explains Emergence Phenomenon And Suggests Discreteness Of Physical Space, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, systems follow the pattern set by the second law of thermodynamics: they evolve from an organized inhomogeneous state into a homogeneous structure-free state. In many other practical situations, however, we observe the opposite emergence phenomenon: in an originally homogeneous structure-free state, an inhomogeneous structure spontaneously appears. In this paper, we show that the analysis of random metric spaces provides a possible explanation for this phenomenon. We also show that a similar analysis supports space-time models in which proper space is discrete.

Why Big-O And Little-O In Algorithm Complexity: A Pedagogical Remark, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the comparative analysis of different algorithm, O- and o-notions are frequently used. While their use is productive, most textbooks do not provide a convincing student-oriented explanation of why these particular notations are useful in algorithm analysis. In this note, we provide such an explanation.

A Corpus For Investigating English-Language Learners' Dialog Behaviors, Nigel Ward, Paola Gallardo

Departmental Technical Reports (CS)

We are interested in developing methods for the semi-automatic discovery of prosodic patterns in dialog and how they differ between languages and among populations. We are starting by examining how the prosody of Spanish-native learners of English differs from that of native speakers. To support this work, we have collected a new corpus of conversations among college students. This includes dialogs between a nonnative speaker of English and a native, dialogs between native speakers of English, and Spanish conversations.

Sometimes, It Is Beneficial To Process Different Types Of Uncertainty Separately, Chrysostomos D. Stylios, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we make predictions based on the measured and/or estimated values of different physical quantities. The accuracy of these predictions depends on the accuracy of the corresponding measurements and expert estimates. Often, for each quantity, there are several different sources of inaccuracy. Usually, to estimate the prediction accuracy, we first combine, for each input, inaccuracies from different sources into a single expression, and then use these expressions to estimate the prediction accuracy. In this paper, we show that it is often more computationally efficient to process different types of uncertainty separately, i.e., to estimate inaccuracies in the …

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 …

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 …

Why Some Families Of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation, Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem of selecting a distribution with the largest possible utility under appropriate constraints. We then show that if we select the utility functional and the constraints which are invariant under natural symmetries -- shift and scaling corresponding to changing the starting point and the measuring unit for describing the corresponding quantity $x$. then the resulting optimal families of probability distributions indeed include most of the …

Once We Know That A Polynomial Mapping Is Rectifiable, We Can Algorithmically Find A Rectification, Julio Urenda, David Finston, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that some polynomial mappings φ: C^k --> Cⁿ are rectifiable in the sense that there exists a polynomial mapping α: Cⁿ --> Cⁿ whose inverse is also polynomial and for which α(φ(z₁, ...,z_k)) = (z₁, ...,z_k, 0, ..., 0) for all z₁, ...,z_k. In many cases, the existence of such a rectification is proven indirectly, without an explicit construction of the mapping α.

In this paper, we use Tarski-Seidenberg algorithm (for deciding the first order theory of real numbers) to design …

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, ..., x_n which are difficult (or even impossible) to measure directly. To estimate these values, we measure easier-to-measure quantities y₁, ..., y_m which are related to the desired quantities by a known relation, and use these measurement results to estimate x_i. 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 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 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 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

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

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

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.