Computer Engineering Commons^™

Granularity Helps Explain Seemingly Irrational Features Of Human Decision Making, Joe Lorkowski, Vladik Kreinovich

Departmental Technical Reports (CS)

Starting from well-known studies by Kahmenan and Tarsky, researchers have found many examples when our decision making -- and our decision making -- seem to be irrational. In this chapter, we show that this seemingly irrational decision making can be explained if we take into account that human abilities to process information are limited; as a result, instead of the exact values of different quantities, we operate with granules that contain these values. On several examples, we show that optimization under such granularity restriction indeed leads to observed human decision making. Thus, granularity helps explain seemingly irrational human decision making.

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.

Interval Computations And Interval-Related Statistical Techniques: Estimating Uncertainty Of The Results Of Data Processing And Indirect Measurements, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we only know the upper bound Δ on the measurement error: |Δx| ≤ Δ. In other words, we only know that the measurement error is located on the interval [−Δ, Δ]. The traditional approach is to assume that Δx is uniformly distributed on [−Δ, Δ]. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such "interval computations" methods have been developed since the 1950s. In this paper, we provide a brief overview of related algorithms and results.

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.

50 Years Of Fuzzy: From Discrete To Continuous To -- Where?, Vladik Kreinovich, Hung T. Nguyen, Olga Kosheleva, Rujira Ouncharoen

Departmental Technical Reports (CS)

While many objects and processes in the real world are discrete, from the computational viewpoint, discrete objects and processes are much more difficult to handle than continuous ones. As a result, a continuous approximation is often a useful way to describe discrete objects and processes. We show that the need for such an approximation explains many features of fuzzy techniques, and we speculate on to which promising future directions of fuzzy research this need can lead us.

How Much For An Interval? A Set? A Twin Set? A P-Box? A Kaucher Interval? Towards An Economics-Motivated Approach To Decision Making Under Uncertainty, Joe Lorkowski, Vladik Kreinovich

Departmental Technical Reports (CS)

A natural idea of decision making under uncertainty is to assign a fair price to different alternatives, and then to use these fair prices to select the best alternative. In this paper, we show how to assign a fair price under different types of uncertainty.

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 …

Is The World Itself Fuzzy? Physical Arguments For -- And Unexpected Computational Consequences Of -- Zadeh's Vision, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Fuzzy methodology has been invented to describe imprecise ("fuzzy") human statements about the world, statements that use imprecise words from natural language like "small" or "large". Usual applications of fuzzy techniques assume that the world itself is ``crisp'', that there are exact equations describing the world, and fuzziness of our statements is caused by the incompleteness of our knowledge. But what if the world itself is fuzzy? What if there is no perfect system of equations describing the physical world -- in the sense that no matter what system of equations we try, there will always be cases when this …

Asymptotically Optimal Algorithm For Checking Whether A Given Vector Is A Solution To A Given Interval-Quantifier Linear System, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have a linear dependence between different quantities. In such situations, we often need to solve the corresponding systems of linear equations. Often, we know the parameters of these equations with interval uncertainty. In this case, depending on the practical problem, we have different notions of a solution. For example, if we determine parameters from observations, we are interested in all the unknowns which satisfy the given system of linear equations for some possible values of the parameters. If we design a system so that it does not exceed given tolerance bounds, then we need to …

If We Take Into Account That Constraints Are Soft, Then Processing Constraints Becomes Algorithmically Solvable, Quentin Brefort, Luc Jaulin, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Constraints are ubiquitous in science and engineering. Constraints describe the available information about the state of the system, constraints describe possible relation between current and future states of the system, constraints describe which future states we would like to obtain. To solve problems from engineering and science, it is therefore necessary to process constraints. We show that if we treat constraints as hard (crisp), with all the threshold values exactly known, then in the general case, all the corresponding computational problems become algorithmically unsolvable. However, these problems become algorithmically solvable if we take into account that in reality, …

Why Ricker Wavelets Are Successful In Processing Seismic Data: Towards A Theoretical Explanation, Afshin Gholamy, Vladik Kreinovich

Departmental Technical Reports (CS)

In many engineering applications ranging from engineering seismology to petroleum engineering and civil engineering, it is important to process seismic data. In processing seismic data, it turns out to be very efficient to describe the signal's spectrum as a linear combination of Ricker wavelet spectra. In this paper, we provide a possible theoretical explanation for this empirical efficiency. Specifically, signal propagation through several layers is discussed, and it is shown that the Ricker wavelet is the simplest non-trivial solution for the corresponding data processing problem, under the condition that the described properties of the approximation family are satisfied.

Likert-Type Fuzzy Uncertainty From A Traditional Decision Making Viewpoint: How Symmetry Helps Explain Human Decision Making (Including Seemingly Irrational Behavior), Joe Lorkowski, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main methods for eliciting the values of the membership function μ(x) is to use the Likert-type scales, i.e., to ask the user to mark his or her degree of certainty by an appropriate mark k on a scale from 0 to n and take μ(x) = k/n. In this paper, we show how to describe this process in terms of the traditional decision making, and we conclude that the resulting membership degrees incorporate both probability and utility information. It is therefore not surprising that fuzzy techniques often work better than probabilistic techniques (which only take into account …

A Catalog Of While Loop Specification Patterns, Aditi Barua, Yoonsik Cheon

Departmental Technical Reports (CS)

This document provides a catalog of while loop patterns along with their skeletal specifications. The specifications are written in a functional form known as intended functions. The catalog can be used to derive specifications of while loops by first matching the loops to the cataloged patterns and then instantiating the skeletal specifications of the matched patterns. Once their specifications are formulated and written, the correctness of while loops can be proved rigorously or formally using the functional program verification technique in which a program is viewed as a mathematical function from one program state to another.

Homotopy Techniques In Solving Systems Of Nonlinear Equations: A Theoretical Justification Of Convex Combinations, Nicholas Sun

Departmental Technical Reports (CS)

One of the techniques for solving systems of non-linear equations F₁(x₁,...,x_n) = 0, ..., F_n(x₁,...,x_n) = 0, (F(x) = 0 in vector notations) is a homotopy method, when we start with a solution of a simplified (and thus easier-to-solve) approximate system G_i(x₁,...,x_n) = 0, and then gradually adjust this solution by solving intermediate systems of equation H_i(x₁,...,x_n) = 0 for an appropriate "transition" function H(x) = f(λ,F(x),G(x)). The success of this method depends on the …

Towards A Formal Description Of Understandability (Causality, Pre-Requisites): From Prosorov's Phonocentric Topology To More General Interior (Closure) Structures, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real life situations, a text consists of related parts; so, to understand a part, we need to first understand some (or all) preceding parts: e.g., to understand Chapter 3, we first need to understand Chapters 1 and 2. In many cases, this dependence is described by a partial order. For this case, O.~Prosorov proposed a natural description of the dependence structure as a topology (satisfying the separation axiom T₀).

In some practical situations, dependence is more general than partial order: e.g., to understand Chapter 3, we may need to understand either Chapter 1 or Chapter 2, …

From Numerical Probabilities To Linguistic Probabilities: A Theoretical Justification Of Empirical Granules Used In Risk Management, Beverly Rivera, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

In many risk management situations, instead of the exact probability values, specialists use a granule to which this probability belongs. Specifically, they use five granules, corresponding to thresholds 10%, 40%, 60%, and 90%. In this paper, we provide an explanation for such non-uniform granulation.

Security Risk Assessment: Towards A Justification For The Security Risk Factor Table Model, Beverly Rivera, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the widely used methods to gauge risk is the Security Risk Factor Table (SRFT) model. While this model has been empirically successful, its use is limited by the fact that its formulas do not have a theoretical explanation -- and thus, there is no guarantee that these formulas will work in other situations as well. In this paper, we provide a theoretical explanation for the SFRT formulas.

If Many Physicists Are Right And No Physical Theory Is Perfect, Then By Using Physical Observations, We Can Feasibly Solve Almost All Instances Of Each Np-Complete Problem, Olga Kosheleva, Michael Zakharevich, Vladik Kreinovich

Departmental Technical Reports (CS)

Many real-life problems are, in general, NP-complete, i.e., informally speaking, are difficult to solve -- at least on computers based on the usual physical techniques. A natural question is: can the use of non-standard physics speed up the solution of these problems? This question has been analyzed for several specific physical theories, e.g., for quantum field theory, for cosmological solutions with wormholes and/or casual anomalies, etc. However, many physicists believe that no physical theory is perfect, i.e., that no matter how many observations support a physical theory, inevitably, new observations will come which will require this theory to be updated. …

Log-Periodic Power Law As A Predictor Of Catastrophic Events: A New Mathematical Justification, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

To decrease the damage caused by meteorological disasters, it is important to be able to predict these disasters as accurately as possible. One of the most promising ways of achieving such a prediction comes from the observation that in the vicinity of a catastrophic event, many parameters exhibit log-periodic power behavior, with oscillations of increasing frequency. By fitting the corresponding formula to the observations, it is often possible to predict the catastrophic event. Such successful predictions were made in many application areas ranging from ruptures of fuel tanks to earthquakes to stock market disruptions. The fact that similar formulas can …

Increased Climate Variability Is More Visible Than Global Warming: A General System-Theory Explanation, Octavio Lerma, Craig Tweedie, Vladik Kreinovich

Departmental Technical Reports (CS)

While global warming is a statistically confirmed long-term phenomenon, its most visible consequence is not the warming itself but, somewhat surprisingly, the increased climate variability. In this paper, we use the general system theory ideas to explain why increased climate variability is more visible than the global warming itself.

How To Estimate Forecasting Quality: A System-Motivated Derivation Of Symmetric Mean Absolute Percentage Error (Smape) And Other Similar Characteristics, Vladik Kreinovich, Hung T. Nguyen, Rujira Ouncharoen

Departmental Technical Reports (CS)

When comparing how well different algorithms forecast time series, researchers use an average value of the ratio |x-y|/(|x|+|y|)/2), known as the Symmetric Mean Absolute Percentage Error (SMAPE). In this paper, we provide a system-motivated explanation for this formula. We also explain how this formula explains the use of geometric mean to combine different forecasts.

Observable Causality Implies Lorentz Group: Alexandrov-Zeeman-Type Theorem For Space-Time Regions, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The famous Alexandrov-Zeeman theorem proves that causality implies Lorentz group. The physical meaning of this result is that once we observe which event can causally affect which other events, then, using only this information, we can reconstruct the linear structure of the Minkowski space-time. The original Alexandrov-Zeeman theorem is based on the causality relation between events represented by points in space-time. Knowing such a point means that we know the exact moment of time and the exact location of the corresponding event - and that this event actually occurred at a single moment of time and at a single spatial …

Possible Geometric Explanations For Basic Empirical Dependencies Of Systems Engineering, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we provide possible geometric explanation for basic empirical dependencies of system engineering: that a properly designed system should have no more than 7 plus minus 2 elements reporting to it, and that the relative cost of correcting a defect on different stages of the system's life cycle is 3--6 on the second (design) stage, 20--100 on the third (development) stage, and 250--1000 on the fourth (production and testing) stage.

How To Explain The Definition Of Stochastic Affiliation To Economics Students, Tonghui Wang, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To formally describe the intuitive idea of "positive correlation" between two quantities, it is often helpful to use the notion of stochastic affiliation. While this notion is useful, its usual definition is not intuitively clear -- which make it difficult to explain this notion to, e.g., economics students. To help students understand this notion, in this paper, we show how the notion of stochastic affiliation can be explained in clear probabilistic terms.

Towards Fast And Reliable Localization Of An Underwater Object: An Interval Approach, Quentin Brefort, Luc Jaulin, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

To localize an underwater object, we measure the distance to this object from several sonar sensors with known locations. The problem is that the signal sent by some of the sonars is reflected not by the desired object(s), but by some auxiliary object and thus, the values measured by these sensors are drastically different from the distance to the desired object. To solve this problem, currently probabilistic methods are used; however, since we do not know the exact probability distributions, these methods may miss the actual location of the object. There exist interval-based methods which provide guaranteed (reliable) bounds on …

Protecting Patient Privacy While Preserving Medical Information For Research, Gang Xiang, Jason O'Rawe, Vladik Kreinovich, Janos Hajagos, Scott Ferson

Departmental Technical Reports (CS)

Patient health records possess a great deal of information that would be useful in medical research, but access to these data is impossible or severely limited because of the private nature of most personal health records. Anonymization strategies, to be effective, must usually go much further than simply omitting explicit identifiers because even statistics computed from groups of records can often be leveraged by hackers to re-identify individuals. Methods of balancing the informativeness of data for research with the information loss required to minimize disclosure risk are needed before these private data can be widely released to researchers who can …

F-Transform Enhancement Of The Sampling Theorem And Reconstruction Of Noisy Signals, Michal Holčapek, Irina Perfilieva, Vladik Kreinovich

Departmental Technical Reports (CS)

According to a sampling theorem, any band-limited and continuous signal can be uniquely reconstructed from certain of its values. We show that a reconstruction can be obtained from the set of F-transform components and moreover, the sampling theorem follows as a particular case. A special attention is paid to the case where sample values of a signal come with noise. We show that in the presence of noise, a more accurate reconstruction than that based on the sampling theorem can be obtained, if instead of noised sample values the F- transform components of the signal with respect to a generalized …

Frequency Selective Surfaces For Extreme Applications, Jay Houston Barton

Open Access Theses & Dissertations

It is known that for high-power microwaves and other extreme environments, the use of resonant metallic elements in frequency selective surfaces can be problematic. The solution developed within this Dissertation to solve these problems was to use guided-mode resonance phenomenon to create all-dielectric frequency selective surfaces that could survive these extreme environments.

To fully understand how these devices work, three different computational electromagnetic methods are formulated and implemented. The formulation of these methods start with the differential form of Maxwellâ??s equation and are derived all the way down to the final simulation state. This is done sequentially and all the …

Multi-Objective Border Patrolling Optimization Using Game Theory And Evolutionary Algorithms, Franciso Oswaldo Aguirre

Open Access Theses & Dissertations

Border security has evolved significantly since the days when no more than 75 Mounted Guards patrolled the U.S. border in the early 1900's. The border region includes thousands of miles of both land and maritime borders that must be controlled, as well as commercial transportation networks. One of the primary components of the Department of Homeland Security (DHS) is the U.S. Customs and Border Protection (CBP) agency. One of the most typical activities performed by CBP is patrolling the expansive open areas in between official points of entry (POEs) to prohibit illegal entry attempts. Roving patrols are routinely conducted by …

An Intelligent System For High Resolution Radar Systems, Janette C. Briones

Open Access Theses & Dissertations

Cognitive radio is a recent, novel approach that integrates machine perception software into wireless systems. The term cognitive radio was first used by Joe Mitola. The concept and the term cognitive radio quickly caught the attention and interest of many in the communications field. Cognitive radios are capable of making decisions and selecting or modifying the operating parameters of a radio. Given these capabilities, it is feasible to build a cognitive radar system as introduced by Simon Haykin in 2006. Cognitive radar, as described by Haykin, is an intelligent system that must be aware of its environment, uses prior knowledge, …