Computer Engineering Commons^™

Statistical And Dempster-Shafer Techniques In Testing Structural Integrity Of Aerospace Structures, Roberto A. Osegueda, Seetharami R. Seelam, Ana C. Holguin, Vladik Kreinovich, Chin-Wang Tao, Hung T. Nguyen

Departmental Technical Reports (CS)

We describe the existing statistics-related methods of testing structural integrity for aerospace structures, describe their drawbacks, how they can be overcome, and compare the resulting techniques.

From Planning To Searching For The Shortest Plan: An Optimal Transition, Raul A. Trejo, Joel Galloway, Charanjiv Sachar, Vladik Kreinovich, Chitta Baral, Le Chi Tuan

Departmental Technical Reports (CS)

Since Kautz and Selman's 1992 ECAI paper on satisfiability based planning, there has been several work on planning through finding models of a logical theory. Most of these works focus on finding a plan of a given length. If we want to find the shortest plan, then usually, we try plans of length 1, 2, ..., until we find the first length for which such a plan exists. When the planning problem is difficult and the shortest plan is of a reasonable length, this linear search can take a long time; to speed up the process, it has been proposed …

A Realistic (Non-Associative) Logic And A Possible Explanations Of 7+-2 Law, Raul A. Trejo, Vladik Kreinovich, I. R. Goodman, Jesus Martinez, Reginaldo Gonzalez

Departmental Technical Reports (CS)

When we know the subjective probabilities (degrees of belief) p1 and p2 of two statements S1 and S2, and we have no information about the relationship between these statements, then the probability of S1&S2 can take any value from the interval [max(p1+p2-1,0),min(p1,p2)]. If we must select a single number from this interval, the natural idea is to take its midpoint. The corresponding "and" operation p1&p_2=(1/2)(max(p1+p2-1,0)+min(p1,p2)) is not associative. However, since the largest possible non-associativity degree |(a&b)&c-a&(b&c)| is equal to 1/9, this non-associativity is negligible if the realistic "granular" degree of belief have granules of width <=1/9. This may explain why humans are most comfortable with <=9 items to choose from (the famous "7 plus minus 2" law).

We also show that the …

Representation, Elicitation, And Aggregation Of Uncertainty In Risk Analysis - From Traditional Probabilistic Techniques To More General, More Realistic Approaches: A Survey, Scott Ferson, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Combining Fuzzy And Probabilistic Knowledge Using Belief Functions, Vladik Kreinovich, Claude Langrand, Hung T. Nguyen

Departmental Technical Reports (CS)

Some knowledge comes in probabilistic terms, some in fuzzy terms. These formalisms are drastically different, so it is difficult to combine the corresponding knowledge. A natural way to combine fuzzy and probabilistic knowledge is to find a formalism which enables us to express both types of knowledge, and then to use a combination rule from this general formalism. In this paper, as such a formalism, we propose to use belief functions. For the case when the universe of discourse is the set of all real numbers, we derive new explicit easy-to-compute analytical formulas for the resulting combination.

Interval Mathematics: Algebraic Aspects, Sompong Dhompongsa, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

Many application-oriented mathematical models deal with real numbers. In real life, due to the inevitable measurement inaccuracy, we do not know the exact values of the measured quantities, we know, at best, the intervals of possible values. It is thus desirable to analyze how the corresponding mathematical results will look if we replace numbers by intervals.

A Statistical Analysis For Rule Base Reduction, Vladik Kreinovich, Claude Langrand, Hung T. Nguyen

Departmental Technical Reports (CS)

When we take into account more input variables in a control system, the number of rules grows exponentially. To decrease the number of rules, we propose not to explicitly state the control for every combination of input variables, but to use the "otherwise" clause. In this paper, we provide a simple statistical analysis of the resulting reduction and show, on a case study, that this reduction can indeed be drastic.

Non-Associative Operations, Bernadette Bouchon-Meunier, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

How is fuzzy logic usually formalized? There are many seemingly reasonable requirements that a logic should satisfy: e.g., since A&B and B&A are the same, the corresponding and-operation should be commutative. Similarly, since A&A means the same as A, we should expect that the and-operation should also satisfy this property, etc. It turns out to be impossible to satisfy all these seemingly natural requirements, so usually, some requirements are picked as absolutely true (like commutativity or associativity), and others are ignored if they contradict to the picked ones. This idea leads to a neat mathematical theory, but the analysis of …

How To Interpret Neural Networks In Terms Of Fuzzy Logic?, Sompong Dhompongsa, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

Neural networks are a very efficient learning tool, e.g., for transforming an experience of an expert human controller into the design of an automatic controller. It is desirable to reformulate the neural network expression for the input-output function in terms most understandable to an expert controller, i.e., by using words from natural language. There are several methodologies for transforming such natural-language knowledge into a precise form; since these methodologies have to take into consideration the uncertainty (fuzziness) of natural language, they are usually called fuzzy logics.

Constrained Fuzzy Arithmetic, Vladik Kreinovich, Mirko Navara, Zdenek Zabokrtsky

Departmental Technical Reports (CS)

No abstract provided.

Aerospace Applications Of Intervals: From Geospatial Data Processing To Fault Detection In Aerospace Structures, Vladik Kreinovich, Scott A. Starks

Departmental Technical Reports (CS)

This paper presents a brief introduction into interval computations and their use in aerospace applications.

Logic-Motivated Choice Of Fuzzy Logic Operators, Pratit Santiprabhob, Hung T. Nguyen, Witold Pedrycz, Vladik Kreinovich

Departmental Technical Reports (CS)

Many different "and"- and "or"-operations have been proposed for use in fuzzy logic; it is therefore important to select, for each particular application, the operations which are the best for this particular application. Several papers discuss the optimal choice of "and"- and "or"-operations for fuzzy control, when the main criterion is to get the stablest control (or the smoothest or the most robust or the fastest-to-compute). In reasoning applications, however, it is more appropriate to select operations which are the best in reflecting human reasoning, i.e., operations which are "the most logical". In this paper, we explain how we can …

Discrete (Set) Derivatives And "Algebraic" Fuzzy Logic Operations, Bernadette Bouchon-Meunier, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

We propose a new way to generalize logical operations from the discrete classical logic to a continuous fuzzy logic; namely, we propose to define derivatives for discrete case, and then to use these derivatives to derive the continuous operations. We show that this natural approach leads to "algebraic" fuzzy operations a*b and a+b-a*b.

Hyperbolic Approach To Fuzzy Control Is Optimal, Hung T. Nguyen, Vladik Kreinovich, Michael Margaliot, Gideon Langholtz

Departmental Technical Reports (CS)

In a series of papers and a book, M. Margaliot and G. Langholz proposed a hyperbolic approach to fuzzy control, in which they apply a certain hyperbolic non-linear transformation to the original variables. In this paper, we consider all possible non-linear transformations of this type and show that this hyperbolic transformation is indeed optimal.

A New Derivation Of Centroid Defuzzification, Mourad Oussalah, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

We describe a new symmetry-based derivation of centroid defuzzification.

Theoretical Justification Of A Heuristic Subbox Selection Criterion, Vladik Kreinovich, Tibor Csendes

Departmental Technical Reports (CS)

The most widely used guaranteed methods for global optimization are probably the interval-based branch-and-bound techniques. In these techniques, we start with a single box - the entire function domain - as a possible location of the global minimum, and then, of each step, subdivide some of the boxes, use interval computations to compute the enclosure [F-(X),F+(X)] of the range f(X) of the objective function f(x) on each new sub-box X, and, based on these computations, eliminate the boxes which cannot contain the global minimum. The computational efficiency of these methods strongly depends on which boxes we select for sub-division. Traditionally, …

Automatic Concurrency In Sequencel, Daniel E. Cooke, Vladik Kreinovich

Departmental Technical Reports (CS)

This paper presents a programming language which we believe to be most appropriate for the automation of parallel data processing, especially data processing of concern to the oil industry and to the U.S. Federal Agencies involved in the analysis of Satellite Telemetry Data. Focus is placed upon major language issues facing the development of the information power grid. The paper presents an example of the type of parallelism desired in the Grid. To implement this parallelism in such a language as Java we need to specify parallelism explicitly. We show that if we rewrite the same solution in the high …

Computational Complexity Of Optimization And Crude Range Testing: A New Approach Motivated By Fuzzy Optimization, G. William Walster, Vladik Kreinovich

Departmental Technical Reports (CS)

It is often important to check whether the maximum max f of a given function f on a given set B is smaller than a given number C. This "crude range testing" (CRT) problem is one of the most important problems in the practical application of interval analysis. Empirical evidence shows that the larger the difference C - max f, the easier the test. In general, the fewer global maxima, the easier the test; and finally, the further away global maxima are from each other, the easier the test. Using standard complexity theory to explain these empirical observations fails because …

Towards Fusing Sophisticated Mathematical Knowledge And Informal Expert Knowledge: An Arbitrary Metric Can Be Naturally Interpreted In Fuzzy Terms, Hung T. Nguyen, Vladik Kreinovich, Witold Pedrycz

Departmental Technical Reports (CS)

In many practical situations, we are faced with a necessity to combine sophisticated mathematical knowledge about the analyzed systems with informal expert knowledge. To make this combination natural, it is desirable to reformulate the abstract mathematical knowledge in understandable intuitive terms. In this paper, we show how this can be done for an abstract metric.

One way to define a metric is to pick certain properties P1, ..., Pn, and to define a similarity between two objects x and y as the degree to which P1(x) is similar to P1(y) and P2(x) is similar to P2(y), etc.

Similarity is naturally …

Second-Order Uncertainty As A Bridge Between Probabilistic And Fuzzy Approaches, Hung T. Nguyen, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

On the example of physics, we show that the traditional one-level description is not completely adequate. For a more adequate structure, a hierarchical description of uncertainty is necessary, which supplements the more traditional first-order uncertainty with second-order, third-order and more sophisticated models. In particular, the second-order approach seems to provide a bridge between probabilistic and fuzzy approaches to uncertainty.

Interval Methods In Remote Sensing: Reliable Sub-Division Of Geological Areas, David D. Coblentz, George R. Keller, Vladik Kreinovich, Jan Beck, Scott A. Starks

Departmental Technical Reports (CS)

No abstract provided.

Towards Automatic Detection Of Erroneous Measurement Results In A Gravity Database, Qian Wen, Ann Q. Gates, Jan Beck, Vladik Kreinovich, George R. Keller

Departmental Technical Reports (CS)

Geospatial databases often contain erroneous measurements. For some such databases such as gravity databases, the known methods of detecting erroneous measurements -- based on regression analysis -- do not work well. As a result, to clean such databases, experts use manual methods which are very time-consuming. In this paper, we propose a (natural) "localized" version of regression analysis as a technique for automatic cleaning. We illustrate the efficiency of this technique on the example of the gravity database.

Localized Regression Analysis As A Method For Detecting Erroneous Measurements In Geospatial Databases, With Application To Gravity Databases, Qian Wen, Nigel Hicks, George R. Keller, Ann Q. Gates, Vladik Kreinovich

Departmental Technical Reports (CS)

Geospatial databases generally consist of measurements related to points (or pixels in the case of raster data), lines, and polygons. In recent years, the size and complexity of these databases have increased significantly and they often contain erroneous measurements or noise. In this paper, we address the problem of detecting erroneous and suspicious values in a database consisting of point measurements. We use a database of measurements of anomalies in the Earth's gravity field that we have complied as a test case, and we found that the standard methods of detecting erroneous measurements - based on regression analysis - do …

2-D Analogues Of Allen Interval Algebra For Image Analysis: Towards Justification, Scott A. Starks, Dima Iourinski, Vladik Kreinovich

Departmental Technical Reports (CS)

In reasoning about time and duration, researchers often use Allen's Interval Algebra. This algebra describes possible relations between 1-D intervals. An interval can precede the other one, follow the other one, start the other one, etc. This algebra describes the relationship between different intervals in terms of words from natural language. To give a natural language description of 2D images, it is desirable to develop a similar approach for describing the relationship between 2-D objects in a picture. In their recent papers, Jim Keller and his collaborators proposed a new approach based on a simulation of a ``force" between these …

Reduction To Independent Variables: From Normal Distribution To General Statistical Case To Fuzzy, Mourad Oussalah, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical problems, we must combine ("fuse") data represented in different formats, e.g., statistical, fuzzy, etc. The simpler the data, the easier to combine them. Therefore, to combine complex data, it is desirable to "decompose" this complex data into simpler (easy-to-combine) data chunks.

It is well known that when we have n random variables x1, ..., xn with a joint Gaussian distribution, then we can reduce them to n independent variables by an appropriate linear transformation x1, ..., xn --> y1 = f1(x1,...,xn), ..., yn = fn(x1,...,xn). It is not so well known but also true that when we …

Automatic Referencing Of Satellite And Radar Images, Sreenath Srikrishnan, Roberto Araiza, Hongjie Xie, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

In order to adequately process satellite and radar information, it is necessary to find the exact correspondence between different types of images and between these images and the existing maps. In other words, we need to reference these images. In this paper, we propose new methods for automatic referencing of satellite and radar images.

Towards More Realistic (E.G., Non-Associative) And- And Or-Operations In Fuzzy Logic, Jesus Martinez, Leopoldo Macias, Ammar Esper, Jesus Chaparro, Vick Alvarado, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

How is fuzzy logic usually formalized? There are many seemingly reasonable requirements that a logic should satisfy: e.g., since A&B and B&A are the same, the corresponding and-operation should be commutative. Similarly, since A&A means the same as A, we should expect that the and-operation should also satisfy this property, etc. It turns out to be impossible to satisfy all these seemingly natural requirements, so usually, some requirements are picked as absolutely true (like commutativity or associativity), and others are ignored if they contradict to the picked ones. This idea leads to a neat mathematical theory, but the analysis of …

Can Computers Do The Job Of Nobelist Physicists? Planck Formula Revisited, Richard Alo, Raul Trejo, Vladik Kreinovich

Departmental Technical Reports (CS)

There exist several computer programs which successfully model the discovery process in science. There are successful expert systems in medicine and other areas. But one area is a real challenge for such systems: theoretical physics. The most advanced knowledge discovery programs (like BACON written under the supervision of the Nobelist Herbert A. Simon) successfully reproduce only 17, 18, and 19 century physics, but stop short of explaining the very first formula of the 20 century: Planck's law of black body radiation. This law, discovered by an insight, led to the modern Quantum Physics. The programs stop short not because the …

Assessing The Predictive Accuracy Of Complex Simulation Models, Timothy Ross, Vladik Kreinovich, Cliff Joslyn

Departmental Technical Reports (CS)

No abstract provided.

Computational Complexity Of Planning With Temporal Goals, Chitta Baral, Vladik Kreinovich, Raul A. Trejo

Departmental Technical Reports (CS)

In the last decade, there has been several studies on the computational complexity of planning. These studies normally assume that the goal of planning is to make a certain fluent true after the sequence of actions. In many real-life planning problems, the goal is represented in a much more complicated temporal form: e.g., in addition to having a desired fluent true at the end, we may want to keep certain fluents true at all times. In this paper, we study the complexity of planning for such temporal goals. We show that for goals expressible in Linear Temporal Logic, planning has …