Engineering Commons^™

Towards Optimal Effort Distribution In Process Design Under Uncertainty, With Application To Education, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most application areas, we need to take care of several (reasonably independent) participants. For example, in controlling economics, we must make sure that all the economic regions prosper. In controlling environment, we want to guarantee that all the geographic regions have healthy environment. In education, we want to make sure that all the students learn all the needed knowledge and skills.

In real life, the amount of resources is limited, so we face the problem of "optimally" distributing these resources between different objects.

What is a reasonable way to formalize "optimally"? For each of the participants, preferences can be …

Optimal Sensor Placement In Environmental Research: Designing A Sensor Network Under Uncertainty, Aline James, Craig Tweedie, Tanja Magoc, Vladik Kreinovich, Martine Ceberio

Departmental Technical Reports (CS)

One of our main challenges in meteorology and environment research is that in many important remote areas, sensor coverage is sparse, leaving us with numerous blind spots. Placement and maintenance of sensors in these areas are expensive. It is therefore desirable to find out how, within a given budget, we can design a sensor network are important activities was developing reasonable techniques for sensor that would provide us with the largest amount of useful information while minimizing the size of the "blind spot" areas which is not covered by the sensors.

This problem is very difficult even to formulate in …

Symmetries: A General Approach To Integrated Uncertainty Management, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

We propose to use symmetries as a general approach to maintaining different types of uncertainty, and we show how the symmetry approach can help, especially in in economics-related applications.

Fuzzy Transforms Of Higher Order Approximate Derivatives: A Theorem, Irina Perfilieva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical applications, it is useful to represent a function f(x) by its fuzzy transform, i.e., by the "average" values over different elements of a fuzzy partition A₁(x), ..., _n(x) (for which A_i(x) >= 0 and A₁(x) + ... + A_n(x) = 1). It is known that when we increase the number n of the partition elements A_i(x), the resulting approximation get closer and closer to the original function: for each value x₀, the values F_i corresponding to the function A_i(x) for …

Checking Design Constraints At Run-Time Using Ocl And Aspectj, Yoonsik Cheon, Carmen Avila, Steve Roach, Cuauhtemoc Munoz

Departmental Technical Reports (CS)

Design decisions and constraints of a software system can be specified precisely using a formal notation such as the Object Constraint Language (OCL). However, they are not executable, and assuring the conformance of an implementation to its design is hard. The inability of expressing design constraints in an implementation and checking them at runtime invites, among others, the problem of design drift and corrosion. We propose runtime checks as a solution to mitigate this problem. The key idea of our approach is to translate design constraints written in a formal notation such as OCL into aspects that, when applied to …

Discrete Taylor Series As A Simple Way To Predict Properties Of Chemical Substances Like Benzenes And Cubanes, Jaime Nava, Vladik Kreinovich, Guillermo Restrepo, Douglas J. Klein

Departmental Technical Reports (CS)

In many applications, we have numerous molecules that are obtained from a "template" molecule like benzene C6H6 or cubane C8H8 by replacing some of its hydrogen atoms with other atoms or atom groups (called ligands). Depending on how many original atoms are replaced and which ones are replaced, we obtain a large number of different chemical substances. It is desirable to be able, based on the measurements performed on a small number of such substances, to accurately predict the characteristics (such as energy) of all similar substances.

Such predictions are very important, since, e.g. cubanes, while kinetically stable, are highly …

From Gauging Accuracy Of Quantity Estimates To Gauging Accuracy And Resolution Of Measuring Physical Fields, Vladik Kreinovich, Irina Perfilieva

Departmental Technical Reports (CS)

For a numerical physical quantity v, because of the measurement imprecision, the measurement result V is, in general, different from the actual value v of this quantity. Depending on what we know about the measurement uncertainty d = V - v, we can use different techniques for dealing with this imprecision: probabilistic, interval, etc.

When we measure the values v(x) of physical fields at different locations x (and/or different moments of time), then, in addition to the same measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location …

A Broad Prospective On Fuzzy Transforms: From Gauging Accuracy Of Quantity Estimates To Gauging Accuracy And Resolution Of Measuring Physical Fields, Vladik Kreinovich, Irina Perfilieva

Departmental Technical Reports (CS)

Fuzzy transform is a new type of function transforms that has been successfully used in different application. In this paper, we provide a broad prospective on fuzzy transform. Specifically, we show that fuzzy transform naturally appears when, in addition to measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.

Model Fusion Under Probabilistic And Interval Uncertainty, With Application To Earth Sciences, Omar Ochoa, Aaron A. Velasco, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most important studies of the earth sciences is that of the Earth's interior structure. There are many sources of data for Earth tomography models: first-arrival passive seismic data (from the actual earthquakes), first-arrival active seismic data (from the seismic experiments), gravity data, and surface waves. Currently, each of these datasets is processed separately, resulting in several different Earth models that have specific coverage areas, different spatial resolutions and varying degrees of accuracy. These models often provide complimentary geophysical information on earth structure (P and S wave velocity structure).

Combining the information derived from each requires a joint …

Automating Java Program Testing Using Ocl And Aspectj, Yoonsik Cheon, Carmen Avila

Departmental Technical Reports (CS)

Random testing can eliminate subjectiveness in constructing test data and increase the diversity of test data. However, one difficult problem is to construct test oracles that decide test results---test failures or successes. Assertions can be used as test oracles and are most effective when derived from formal specifications such as OCL constraints. If fully automated, random testing can reduce the cost of testing dramatically. In this paper we propose an approach for automating Java program testing by combining random testing and OCL. The key idea of our approach is to use OCL constraints as test oracles by translating them to …

Astronomical Tests Of Relativity: Beyond Parameterized Post-Newtonian Formalism (Ppn), To Testing Fundamental Principles, Vladik Kreinovich

Departmental Technical Reports (CS)

By the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.

Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. …

Continuous If-Then Statements Are Computable, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we must compute the value of an if-then expression f(x) defined as "if c(x) >= 0 then f₊(x) else f_-(x)", where f₊(x), f_-(x), and c(x) are computable functions. The value f(x) cannot be computed directly, since in general, it is not possible to check whether a given real number c(x) is non-negative or non-positive. Similarly, it is not possible to compute the value f(x) if the if-then function is discontinuous, i.e., when f₊(x₀) =/= f_-(x₀) for some x₀ for …

Why Tensors?, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

We show that in many application areas including soft constraints reasonable requirements of scale-invariance lead to polynomial (tensor-based) formulas for combining degrees (of certainty, of preference, etc.)

Symmetry Between True, False, And Uncertain: An Explanation, Eulalia Szmidt, Vladik Kreinovich

Departmental Technical Reports (CS)

In intuitionistic fuzzy sets, there is a natural symmetry between degrees of truth and falsity. As a result, for such sets, natural similarity measures are symmetric relative to an exchange of true and false values. It has been recently shown that among such measures, the most intuitively reasonable are the ones which are also symmetric relative to an arbitrary permutation of degrees of truth, falsity, and uncertainty. This intuitive reasonableness leads to a conjecture that such permutations are not simply mathematical constructions, that these permutations also have some intuitive sense. In this paper, we show that each such permutation can …

"Weird" Fuzzy Notations: An Algebraic Interpretation, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, fuzzy logic used non-standard notations like m₁/x₁ + ... + m_n/x_n for a function that attains the value m₁ at x₁, ..., and the value m_n at x_n. In this paper, we provide an algebraic explanation for these notations.

Diagonalization Is Also Practically Useful: A Geometric Idea, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

On The Use Of Abstract Workflows To Capture Scientific Process Provenance, Paulo Pinheiro Da Silva, Leonardo Salayandia, Nicholas Del Rio, Ann Q. Gates

Departmental Technical Reports (CS)

Capturing provenance about artifacts produced by distributed scientific processes is a challenging task. For example, one approach to facilitate the execution of a scientific process in distributed environments is to break down the process into components and to create workflow specifications to orchestrate the execution of these components. However, capturing provenance in such an environment, even with the guidance of orchestration logic, is difficult because of important details that may be hidden by the component abstractions. In this paper, we show how to use abstract workflows to systematically enhance scientific processes to capture provenance at appropriate levels of detail. Abstract …

From Interval Computations To Constraint-Related Set Computations: Towards Faster Estimation Of Statistics And Odes Under Interval And P-Box Uncertainty, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Square Root Of "Not": A Major Difference Between Fuzzy And Quantum Logics, Vladik Kreinovich, Ladislav J. Kohout, Eunjin Kim

Departmental Technical Reports (CS)

Many authors have mentioned the similarity between quantum logic and fuzzy logic. In this paper, we show that, in spite of this similarity, these logics are not identical. Specifically, we emphasize that while quantum logic has a special ``square root of not'' operation which is very useful in quantum computing, fuzzy logic lacks such an operation.

Quantum Computations Techniques For Gauging Reliability Of Interval And Fuzzy Data, Luc Longpre, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

In traditional interval computations, we assume that the interval data corresponds to guaranteed interval bounds, and that fuzzy estimates provided by experts are correct. In practice, measuring instruments are not 100% reliable, and experts are not 100% reliable, we may have estimates which are "way off", intervals which do not contain the actual values at all. Usually, we know the percentage of such outlier un-reliable measurements. However, it is desirable to check that the reliability of the actual data is indeed within the given percentage. The problem of checking (gauging) this reliability is, in general, NP-hard; in reasonable cases, there …

Engineering Design Under Imprecise Probabilities: Computational Complexity, Vladik Kreinovich

Departmental Technical Reports (CS)

In engineering design problems, we want to make sure that a certain quantity c of the designed system lies within given bounds -- or at least that the probability of this quantity to be outside these bounds does not exceed a given threshold. We may have several such requirements -- thus the requirement can be formulated as bounds [Fc(x); Fc(x)] on the cumulative distribution function Fc(x) of the quantity c; such bounds are known as a p-box.

The value of the desired quantity c depends on the design parameters a and the parameters b characterizing the environment: c = f(a; …

Looking For Entropy Rate Constancy In Spoken Dialog, Alejandro Vega, Nigel Ward

Departmental Technical Reports (CS)

The entropy constancy principle describes the tendency for information in language to be conveyed at a constant rate. We explore the possible role of this principle in spoken dialog, using the ``summed entropy rate,'' that is, the sum of the entropies of the words of both speakers per second of time. Using the Switchboard corpus of casual dialogs and a standard ngram language model to estimate entropy, we examine patterns in entropy rate over time and the distribution of entropy across the two speakers. The results show effects that can be taken as support for the principle of constant entropy, …

Probabilistic Interpretation Of Fuzzy Transforms And Fuzzy Control, Irina Perfilieva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical applications, it turns out to be useful to use the notion of fuzzy transform: once we have non-negative functions A₁(x), ..., A_n(x), with A₁(x) + ... + A_n(x) = 1, we can then represent each function f(x) by the coefficients F_i which are defined as the ratio of two integrals: of f(x) * A_i(x) and of A_i(x). Once we know the coefficients F_i, we can (approximately) reconstruct the original function f(x) as F₁ * A₁(x) + ... + F …

Measurement's Result And Its Error As Fuzzy Variables: Background And Perspectives, Gennady N. Solopchenko, Konstantin K. Semenov, Vladik Kreinovich, Leon Reznik

Departmental Technical Reports (CS)

The possibility of using fuzzy variables for describing measurands and their error characteristics is investigated. The elementary arithmetic operations within the limits of such representation are considered.

Equations Without Equations: Challenges On A Way To A More Adequate Formalization Of Causality Reasoning In Physics, Roberto Araiza, Vladik Kreinovich, Juan Ferret

Departmental Technical Reports (CS)

Not all mathematical solutions to physical equations are physically meaningful: e.g., if we reverse all the molecular velocities in a breaking cup, we get pieces self-assembling into a cup. The resulting initial conditions are "degenerate": once we modify them, self-assembly stops. So, in a physical solution, the initial conditions must be "non-degenerate".

A challenge in formalizing this idea is that it depends on the representation. Example 1: we can use the Schroedinger equation to represent the potential field V(x)=F(f,...) as a function of the wave function f(x,t) and its derivatives. The new equation dF/dt=0 is equivalent to the Schroedinger equation, …

Analysis Of Information And Computation In Physics Explains Cognitive Paradigms: From Full Cognition To Laplace Determinism To Statistical Determinism To Modern Approach, Vladik Kreinovich, Roberto Araiza, Juan Ferret

Departmental Technical Reports (CS)

In this paper, we analyze the problem of prediction in physics from the computational viewpoint. We show that physical paradigms like Laplace determinism, statistical determinism, etc., can be naturally explained by this computational analysis. In our explanations, we use the notions of the Algorithmic Information Theory such as Kolmogorov complexity and algorithmic randomness, as well as the novel, more physics-oriented variants of these notions.

Towards Dynamical Systems Approach To Fuzzy Clustering, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many application areas, there is a need for clustering, and there is a need to take fuzzy uncertainty into account when clustering. Most existing fuzzy clustering techniques are based on the idea that an object belongs to a certain cluster if this object is close to a typical object from this cluster. In some application areas, however, this idea does not work well. One example of such application is clustering in education that is used to convert a detailed number grade into a letter grade.

In such application, it is more appropriate to use clustering techniques which are based …

From Interval Computations To Constraint-Related Set Computations: Towards Faster Estimation Of Statistics And Odes Under Interval, P-Box, And Fuzzy Uncertainty, Martine Ceberio, Vladik Kreinovich, Andrzej Pownuk, Barnabas Bede

Departmental Technical Reports (CS)

In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. In our previous papers, we proposed an extension of this technique to set computations, where on each stage, in addition to intervals of possible values of the quantities, we also keep sets of possible values of pairs (triples, etc.). In this paper, we show that in several practical problems, such as estimating statistics (variance, correlation, etc.) and solutions to ordinary differential equations (ODEs) with given accuracy, this new formalism enables us to find estimates in feasible (polynomial) time.

Expert Knowledge Is Needed For Design Under Uncertainty: For P-Boxes, Backcalculation Is, In General, Np-Hard, Vladik Kreinovich

Departmental Technical Reports (CS)

In engineering design problems, we want to make sure that a certain quantity c of the designed system lies within given bounds -- or at least that the probability of this quantity to be outside these bounds does not exceed a given threshold. We may have several such requirements -- thus the requirement can be formulated as bounds on the cumulative distribution function F(x) of the quantity c; such bounds are known as a p-box.

The value of the desired quantity c depends on the design parameters a and the parameters b characterizing the environment: c=f(a,b). To achieve the design …

What Is The Best Way To Distribute Efforts Among Students: Towards Quantitative Approach To Human Cognition, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In a typical class, we have students at different levels of knowledge, student with different ability to learn the material. In the ideal world, we should devote unlimited individual attention to all the students and make sure that everyone learns all the material. In real life, our resources are finite. Based on this finite amount of resources, what is the best way to distribute efforts between different students?

Even when we know the exact way each student learns, the answer depends on what is the objective of teaching the class. This can be illustrated on two extreme example: If the …