Computer Engineering Commons^™

Error Estimations For Indirect Measurements: Randomized Vs. Deterministic Algorithms For "Black-Box" Programs, Vladik Kreinovich, Raul A. Trejo

Departmental Technical Reports (CS)

In many real-life situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure them indirectly: by first measuring some relating quantities x1,...,xn, and then by using the known relation between xi and y to reconstruct the value of the desired quantity y.

In practice, it is often very important to estimate the error of the resulting indirect measurement. In this paper, …

Chu Spaces: Towards New Justification For Fuzzy Heuristics, Nhu Nguyen, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc.

On Granularity In Fuzzy Logic: Minimum And Maximum Are The Only Absolutely Granular T-Norm And T-Conorm, Vladik Kreinovich, Bernadette Bouchon-Meunier

Departmental Technical Reports (CS)

No abstract provided.

Complex Fuzzy Sets: Towards New Foundations, Hung T. Nguyen, Abraham Kandel, Vladik Kreinovich

Departmental Technical Reports (CS)

Uncertainty of complex-valued physical quantities z=x+iy can be described by complex fuzzy sets. Such sets can be described by membership functions m(x,y) which map the universe of discourse (complex plane) into the interval [0,1]. The problem with this description is that it is difficult to directly translate into words from natural language. To make this translation easier, several authors have proposed to use, instead of a single membership function for describing the complex number, several membership functions which describe different real-valued characteristics of this numbers, such as its real part, its imaginary part, its absolute value, etc. The quality of …

Shadows Of Fuzzy Sets - A Natural Approach Towards Describing 2-D And Multi-D Fuzzy Uncertainty In Linguistic Terms, Hung T. Nguyen, Berlin Wu, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy information processing systems start with expert knowledge which is usually formulated in terms of words from natural language. This knowledge is then usually reformulated in computer-friendly terms of membership functions, and the system transform these input membership functions into the membership functions which describe the result of fuzzy data processing. It is then desirable to translate this fuzzy information back from the computer-friendly membership functions language to the human-friendly natural language. In general, this is difficult even in a 1-D case, when we are interested in a single quantity y; however, the fuzzy research community has accumulated some expertise …

Which Sensor Set Is Better For Monitoring Spacecraft Subsystems? A Geometric Answer And Its Probabilistic Generalization, Matthew Barry, Vladik Kreinovich

Departmental Technical Reports (CS)

Each Space Shuttle mission produces more than 25,000 real-time measurements in NASA's mission control center. Within the mission control center, dozens of computer programs analyze these measurements and present results to mission control personnel. Because these programs support the practice of human-in-the-loop control, they serve primarily to present information to mission controllers. The controller's job is to interpret the displayed information to monitor spacecraft and astronaut performance, taking decisions and control actions when necessary for mission success or crew safety.

A single mission controller clearly cannot monitor all 25,000 real-time measurements. The experience of human space flight has evolved into …

Intelligent Mining In Image Databases, With Applications To Satellite Imaging And To Web Search, Stephen Gibson, Vladik Kreinovich, Luc Longpre, Brian Penn, Scott A. Starks

Departmental Technical Reports (CS)

An important part of our knowledge is in the form of images. For example, a large amount of geophysical and environmental data comes from satellite photos, a large amount of the information stored on the Web is in the form of images, etc. It is therefore desirable to use this image information in data mining. Unfortunately, most existing data mining techniques have been designed for mining numerical data and are thus not well suited for image databases. Hence, new methods are needed for image mining. In this paper, we show how data mining can be used to find common patterns …

Choosing A Physical Model: Why Symmetries?, Raul A. Trejo, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

No abstract provided.

Discrete (Granular) Logics: A New (Natural) Notion Of Continuity, With A Complete Description Of All Continuous Granular Logics, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

In most knowledge-based systems, the experts' uncertainty is described by a real number from the interval [0,1] (this number is called subjective probability, degree of certainty, etc.). However, experts usually use a small finite set of words to describe their degree of unecratinty; thus, to adequately describe the expert's optinion, it is desirable to use a finite (granular) logic. If all we know about the expert's opinion on two statements A and B is this expert's degrees of certainty d(A) and d(B) in these two statements, and the user asks a query "A and B?", then we need to estimate …

Computational Complexity Of Planning, Diagnosis, And Diagnostic Planning In The Presence Of Static Causal Laws, Chitta Baral, Le Chi Tuan, Vladik Kreinovich

Departmental Technical Reports (CS)

Planning is a very important AI problem, and it is also a very time-consuming AI problem. To get an idea of how complex different planning problems are, it is useful to describe the computational complexity of different general planning problems. This complexity has been described for problems in which the result res(a,s) of applying an action a to a system in a state s is uniquely determined by the action a and by the state s. In real-life planning, some consequences of certain actions are non-deterministic. In this paper, we expand the known results about computational complexity of planning (with …

Invariance-Based Justification Of The Maximum Entropy Method And Of Generalized Maximum Entropy Methods In Data Processing, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Maximum entropy method and its generalizations are very useful in data processing. In this paper, we show that these methods naturally follow from reasonable invariance requirements.

Aircraft Integrity And Reliability, Carlos M. Ferregut, Roberto A. Osegueda, Yohanz Mendoza, Vladik Kreinovich, Timothy J. Ross

Departmental Technical Reports (CS)

In his recent paper "Probability theory needs an infusion of fuzzy logic to enhance its ability to deal with real-world problems", L. A. Zadeh explains that probability theory needs an infusion of fuzzy logic to enhance its ability to deal with real-world problems. In this paper, we give an example of a real-world problem for which such an infusion is indeed successful: the problems of aircraft integrity and reliability.