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 Soft computing (2)
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 And Mountain method (1)
 NonGaussian distributions (1)
 Empirical measurement practice (1)
 Fuzzy measure (1)
 Approximating fuzzy sets by crisp sets (1)
 Cartesian presentation (1)
 Two sigma rule (1)
 Pain relief (1)
 Foundations (1)
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 Fuzzy sparse rule base (1)
 "shadowed" fuzzy sets (1)
 Uncertainty (1)
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 Expert knowledge (1)
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Articles 1  30 of 42
FullText Articles in Computer Engineering
Itanium's New Basic Operation Of Fused MultiplyAdd: Theoretical Explanation And Theoretical Challenge, Vladik Kreinovich
Itanium's New Basic Operation Of Fused MultiplyAdd: Theoretical Explanation And Theoretical Challenge, Vladik Kreinovich
Departmental Technical Reports (CS)
A new Intel's 64bit chip Itanium has a new instruction set which includes a fused multiplyadd instruction x1+x2*x3. In this short article, we explain the empirical reasons behind the choice of this instruction, give possible theoretical explanation for this choice, and mention a related theoretical challenge.
Strassen's Algorithm Made (Somewhat) More Natural: A Pedagogical Remark, Ann Q. Gates, Vladik Kreinovich
Strassen's Algorithm Made (Somewhat) More Natural: A Pedagogical Remark, Ann Q. Gates, Vladik Kreinovich
Departmental Technical Reports (CS)
Strassen's 1969 algorithm for fast matrix multiplication is based on the possibility to multiply two 2 x 2 matrices A and B by using 7 multiplications instead of the usual 8. The corresponding formulas are an important part of any algorithms course, but, unfortunately, even in the best textbook expositions. they look very ad hoc. In this paper, we show that the use of natural symmetries can make these formulas more natural.
Geombinatorics Of "Smart Dust", Edward Vidal, Luc Longpre, Vladik Kreinovich, Huang Haitao
Geombinatorics Of "Smart Dust", Edward Vidal, Luc Longpre, Vladik Kreinovich, Huang Haitao
Departmental Technical Reports (CS)
Smart Dust is a collection of small sensorequipped leaves which send their information to two or more receivers. When a receiver gets a signal from a sensor, it can determine the direction from which this signal came. By combining the directions from two different receivers, we can determine the 3D locations of all the leaves, and thus, transform their sensor readings into a 3D picture of the corresponding parameters (temperature, moisture, etc.). The more leaves we send, the more information we gather. However, since the direction can only be measured with a certain accuracy, when we send too many leaves ...
Aerospace Applications Of Soft Computing And Interval Computations (With An Emphasis On Simulation And Modeling), Scott A. Starks, Vladik Kreinovich
Aerospace Applications Of Soft Computing And Interval Computations (With An Emphasis On Simulation And Modeling), Scott A. Starks, Vladik Kreinovich
Departmental Technical Reports (CS)
This paper presents a brief overview of our research in applications of soft computing and interval computations to aerospace problems, with a special emphasis on simulation and modeling.
Optimal Elimination Of Inconsistency In Expert Knowledge: Formulation Of The Problem, Fast Algorithms, Timothy J. Ross, Berlin Wu, Vladik Kreinovich
Optimal Elimination Of Inconsistency In Expert Knowledge: Formulation Of The Problem, Fast Algorithms, Timothy J. Ross, Berlin Wu, Vladik Kreinovich
Departmental Technical Reports (CS)
Expert knowledge is sometimes inconsistent. In this paper, we describe the problem of eliminating this inconsistency as an optimization problem, and present fast algorithms for solving this problem.
On Approximation Of Fuzzy Sets By Crisp Sets: From Continuous ControlOriented Defuzzification To Discrete Decision Making, Hung T. Nguyen, Witold Pedrycz, Vladik Kreinovich
On Approximation Of Fuzzy Sets By Crisp Sets: From Continuous ControlOriented Defuzzification To Discrete Decision Making, Hung T. Nguyen, Witold Pedrycz, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that the necessity to make crisp decisions in uncertain (fuzzy) situations leads to the necessity to "approximate" fuzzy sets by crisp sets. We show that seemingly natural approximation ideas  such as using alphacut for a given alpha  often do not work, and we describe new approximations which not only work, but which are optimal in some reasonable sense
On The Optimal Choice Of Quality Metric In Image Compression A Soft Computing Approach, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich, Liya Ding
On The Optimal Choice Of Quality Metric In Image Compression A Soft Computing Approach, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich, Liya Ding
Departmental Technical Reports (CS)
In a lossy compression, the reconstructed image I' differs from the original image I. In different situations, different compressions lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. It's natural to select the compression method for which the average value of some quality metric d(I,I') is the smallest. Which quality metric should we choose? We show that under reasonable symmetry conditions, L^p metrics d(I,I')=integral of I(x)I'(x)^p are the best, and how to compute the optimal value of p from the ...
Fuzzy Logic And Its Applications In Medicine, Nguyen Hoang Phuong, Vladik Kreinovich
Fuzzy Logic And Its Applications In Medicine, Nguyen Hoang Phuong, Vladik Kreinovich
Departmental Technical Reports (CS)
Fuzzy set theory and fuzzy logic are a highly suitable and applicable basis for developing knowledgebased systems in medicine for tasks such as the interpretation of sets of medical findings, syndrome differentiation in Eastern medicine, diagnosis of diseases in Western medicine, mixed diagnosis of Integrated western and Eastern medicine, the optimal selection of medical treatments integrating western and eastern medicine, and for realtime monitoring of patient data etc. This was verified by trials with the following systems which were developed by our group in Vietnam: a fuzzy Expert System for Syndromes Differentiation in Oriental Traditional Medicine, an Expert System for ...
Computational Complexity Of Planning And Approximate Planning In Presence Of Incompleteness, Chitta Baral, Vladik Kreinovich, Raul Trejo
Computational Complexity Of Planning And Approximate Planning In Presence Of Incompleteness, Chitta Baral, Vladik Kreinovich, Raul Trejo
Departmental Technical Reports (CS)
In the last several years, there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation. Recently, there has been proposal to use "sensing" actions to plan in presence of incompleteness. In this paper we study the complexity of planning in such cases. In our study we use the action description language A proposed in 1991 by Gelfond and Lifschitz, and its extensions.
It is known that if we consider only plans of feasible (polynomial) length, planning  with complete information about the initial situation  in A is NPcomplete ...
Why 95% And Two Sigma? A Theoretical Justification For An Empirical Measurement Practice, Hung T. Nguyen, Vladik Kreinovich, ChinWang Tao
Why 95% And Two Sigma? A Theoretical Justification For An Empirical Measurement Practice, Hung T. Nguyen, Vladik Kreinovich, ChinWang Tao
Departmental Technical Reports (CS)
The probability p(k) that the value of a random variable is far away from the mean (e.g. further than k standard deviations away) is so small that this possibility can be often safely ignored. It is desirable to select k for which the dependence of the probability p(k) on the distribution is the smallest possible. Empirically, this dependence is the smallest for k between 1.5 and 2.5. In this paper, we give a theoretical explanation for this empirical result.
On Representation And Approximation Of Operations In Boolean Algebras, I. R. Goodman, Vladik Kreinovich
On Representation And Approximation Of Operations In Boolean Algebras, I. R. Goodman, Vladik Kreinovich
Departmental Technical Reports (CS)
Several universal approximation and universal representation results are known for nonBoolean multivalued logics such as fuzzy logics. In this paper, we show that similar results can be proven for multivalued Boolean logics as well.
Extracting Fuzzy Sparse Rule Base By Cartesian Representation And Clustering, Yeung Yam, Vladik Kreinovich, Hung T. Nguyen
Extracting Fuzzy Sparse Rule Base By Cartesian Representation And Clustering, Yeung Yam, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
Sparse rule base and interpolation have been proposed as possible solution to alleviate the geometric complexity problem of large fuzzy set. However, no formal method to extract sparse rule base is yet available. This paper combines the recently introduced Cartesian representation of membership functions and a mountain methodbased clustering technique for extraction. A case study is included to demonstrate the effectiveness of the approach.
A New Universal Approximation Result For Fuzzy Systems, Which Reflects CnfDnf Duality, Irina Perfilieva, Vladik Kreinovich
A New Universal Approximation Result For Fuzzy Systems, Which Reflects CnfDnf Duality, Irina Perfilieva, Vladik Kreinovich
Departmental Technical Reports (CS)
There are two main fuzzy system methodologies for translating expert rules into a logical formula: In Mamdani's methodology, we get a DNF formula (disjunction of conjunctions), and in a methodology which uses logical implications, we get, in effect, a CNF formula (conjunction of disjunctions). For both methodologies, universal approximation results have been proven which produce, for each approximated function f(x), two different approximating relations RDNF(x,y) and RCNF(x,y). Since in fuzzy logic, there is a known relation FCNF(x)<=FDNF(x) between CNF and DNF forms of a propositional formula F, it is reasonable to expect that we would be able to prove the existence of approximations for which a similar relation RCNF(x,y)<=RDNF(x,y) holds. Such existence is proved in our paper.
On The Optimal Choice Of Quality Metric In Image Compression, Olga Kosheleva, Vladik Kreinovich, Yeung Yam
On The Optimal Choice Of Quality Metric In Image Compression, Olga Kosheleva, Vladik Kreinovich, Yeung Yam
Departmental Technical Reports (CS)
No abstract provided.
Asymptotically Optimal Algorithms For Weather Applications Of Smart Dust, Edward Vidal, Luc Longpre, Vladik Kreinovich, Huang Haitao, Yeung Yam
Asymptotically Optimal Algorithms For Weather Applications Of Smart Dust, Edward Vidal, Luc Longpre, Vladik Kreinovich, Huang Haitao, Yeung Yam
Departmental Technical Reports (CS)
No abstract provided.
Some Practical Applications Of Soft Computing And Data Mining, Hung T. Nguyen, Nadipuram R. Prasad, Vladik Kreinovich, Habib Gassoumi
Some Practical Applications Of Soft Computing And Data Mining, Hung T. Nguyen, Nadipuram R. Prasad, Vladik Kreinovich, Habib Gassoumi
Departmental Technical Reports (CS)
Traditional data mining techniques mainly deal with a search for patterns in traditional databases, where data consists of numbers and words. In many application areas, however, data is more complicated: reallife data is often obtained as an image from a camera rather than a few measurements. Furthermore, this image can also change dynamically. In this paper, we present several examples of how soft computing is related to mining such data.
Towards Reliable SubDivision Of Geological Areas: Interval Approach, David D. Coblentz, Vladik Kreinovich, Brian S. Penn, Scott A. Starks
Towards Reliable SubDivision Of Geological Areas: Interval Approach, David D. Coblentz, Vladik Kreinovich, Brian S. Penn, Scott A. Starks
Departmental Technical Reports (CS)
An appropriate subdivision of a geophysical area into segments enables us to extrapolate the results obtained in some locations within the segment (where extensive research was done) to other locations within the same segment, and thus, get a good understanding of the locations which weren't thoroughly analyzed.
Often, different evidence and different experts' intuition support different subdivisions schemes. For example, in our area  Rio Grande rift zone  there is some geochemical evidence that this zone is divided into three segments, but, in the viewpoint of many researchers, this evidence is not yet sufficiently convincing.
We show that if we ...
Computational Complexity Of Planning Based On Partial Information About The System's Present And Past States, Chitta Baral, Le Chi Tuan, Raul A. Trejo, Vladik Kreinovich
Computational Complexity Of Planning Based On Partial Information About The System's Present And Past States, Chitta Baral, Le Chi Tuan, Raul A. Trejo, Vladik Kreinovich
Departmental Technical Reports (CS)
Planning is a very important AI problem, and it is also a very timeconsuming 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 planning is based on the (complete or partial) information about the current state of the system. In reallife planning, in addition to this information, we often also use the knowledge about the system's past behavior. To describe such more realistic planning situations, a special language L was developed in 1997 ...
How Important Is Theory For Practical Problems? A Partial Explanation Of Hartmanis' Observation, Vladik Kreinovich, Luc Longpre
How Important Is Theory For Practical Problems? A Partial Explanation Of Hartmanis' Observation, Vladik Kreinovich, Luc Longpre
Departmental Technical Reports (CS)
No abstract provided.
Granularity As An Optimal Approach To Uncertainty  A General Mathematical Idea With Applications To Sleep, Consumption, Traffic Control, Learning, Etc., Vladik Kreinovich, Hung T. Nguyen
Granularity As An Optimal Approach To Uncertainty  A General Mathematical Idea With Applications To Sleep, Consumption, Traffic Control, Learning, Etc., Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
Traditional statistical and fuzzy approaches to describing uncertainty are continuous in the sense that we use a (potentially infinite) set of values from the interval [0,1] to characterize possible degrees of uncertainty. In reality, experts describe their degree of belief by using one of the finitely many words from natural language; in this sense, the actual description of expert uncertainty is granular.
In this paper, we show that in some reasonable sense, granularity is the optimal way of describing uncertainty. A similar mathematical idea explains similar "granularity" in such diverse areas as sleep, consumption, traffic control, and learning.
A New Graph Characteristic And Its Application To Numerical Computability, Frank Harary, Vladik Kreinovich, Luc Longpre
A New Graph Characteristic And Its Application To Numerical Computability, Frank Harary, Vladik Kreinovich, Luc Longpre
Departmental Technical Reports (CS)
Many traditional numerical algorithms include a step on which we check whether a given real number a is equal to 0. This checking is easy for rational numbers, but for constructive real numbers, whether a number is 0 or not is an algorithmically undecidable problem. It is therefore desirable to reformulate the existing algorithms with as few such comparisons as possible. We describe a new graph characteristic; this characteristic describes how the number of comparisons in an algorithm can be reduced.
The Use Of Fuzzy Measures In Pain Relief Control, Vladik Kreinovich, Nadipuram R. Prasad
The Use Of Fuzzy Measures In Pain Relief Control, Vladik Kreinovich, Nadipuram R. Prasad
Departmental Technical Reports (CS)
Many people suffer from a continuous strong pain which is caused solely by the malfunction of the pain mechanism itself. One way to ease their pain is to electrically stimulate the spinal cord. Since the equations of pain are not known, we must use heuristic methods to find the optimal pain relief stimulation. In this paper, we show how fuzzy measures and similar nonlinear models can be used in pain relief control: they can be used to determine the parameters of the model which describes the dependence of the pain relief on the applied stimulation. Thus, fuzzy measures lead to ...
A Comment On The Shape Of The Solution Set For Systems Of Interval Linear Equations With Dependent Coefficients, Goetz Alefeld, Vladik Kreinovich, Guenter Mayer, Michael Huth
A Comment On The Shape Of The Solution Set For Systems Of Interval Linear Equations With Dependent Coefficients, Goetz Alefeld, Vladik Kreinovich, Guenter Mayer, Michael Huth
Departmental Technical Reports (CS)
This article is a short supplement to our previously published paper, in which we prove that each semialgebraic set can be represented as a projection of a solution set of some system of linear equations with dependent coefficients. The new results says that interval occurring can be chosen as narrow as wanted. This new result is proven by a simple linear transformation.
Why Two Sigma? A Theoretical Justification, Hung T. Nguyen, Vladik Kreinovich, Gennady N. Solopchencko, ChingWang Tao
Why Two Sigma? A Theoretical Justification, Hung T. Nguyen, Vladik Kreinovich, Gennady N. Solopchencko, ChingWang Tao
Departmental Technical Reports (CS)
For a normal distribution, the probability density is everywhere positive, so in principle, all real numbers are possible. In reality, the probability that a random variable is far away from the mean is so small that this possibility can be often safely ignored. Usually, a small real number k is picked (e.g., 2 or 3); then, with a probability P0(k)~1 (depending on k), the normally distributed random variable with mean a and standard deviation sigma belongs to the interval A=[ak*sigma,a+k*sigma].
The actual error distribution may be nonGaussian; hence, the probability P(k ...
Integrating Domain Knowledge With Data: From Crisp To Probabilistic And Fuzzy Knowledge, Hung T. Nguyen, Vladik Kreinovich, Leonid Reznik
Integrating Domain Knowledge With Data: From Crisp To Probabilistic And Fuzzy Knowledge, Hung T. Nguyen, Vladik Kreinovich, Leonid Reznik
Departmental Technical Reports (CS)
It is well known that prior knowledge about the domain can improve (often drastically) the accuracy of the estimates of the physical quantities in comparison with the estimates which are solely based on the measurement results. In this paper, we show how a known method of integrating crisp domain knowledge with data can be (naturally) extended to the case when the domain knowledge is described in statistical or fuzzy terms.
Fuzzy (Granular) Levels Of Quality, With Applications To Data Mining And To Structural Integrity Of Aerospace Structures, Roberto A. Osegueda, Carlos Ferregut, Vladik Kreinovich, Seelam Seetharami, Harry Schulte
Fuzzy (Granular) Levels Of Quality, With Applications To Data Mining And To Structural Integrity Of Aerospace Structures, Roberto A. Osegueda, Carlos Ferregut, Vladik Kreinovich, Seelam Seetharami, Harry Schulte
Departmental Technical Reports (CS)
Experts usually describe quality by using words from natural language such as "perfect", "good", etc. In this paper, we deduce natural numerical values corresponding to these words, and show that these values explain empirical dependencies uncovered in data mining and in the analysis of structural integrity of aerospace structures.
Towards Feasible Approach To Plan Checking Under Probabilistic Uncertainty: Interval Methods, Raul A. Trejo, Vladik Kreinovich, Chitta Baral
Towards Feasible Approach To Plan Checking Under Probabilistic Uncertainty: Interval Methods, Raul A. Trejo, Vladik Kreinovich, Chitta Baral
Departmental Technical Reports (CS)
The main problem of planning is to find a sequence of actions that an agent must perform to achieve a given objective. An important part of planning is checking whether a given plan achieves the desired objective. Historically, in AI, the planning and plan checking problems were mainly formulated and solved in a deterministic environment, when the initial state is known precisely and when the results of each action in each state is known (and uniquely determined). In this deterministic case, planning is difficult, but plan checking is straightforward. In many reallife situations, we only know the probabilities of different ...
Towards Optimal Mosaicking Of MultiSpectral Images, Francisco Garcia, Roberto Araiza, Brain Rzycki
Towards Optimal Mosaicking Of MultiSpectral Images, Francisco Garcia, Roberto Araiza, Brain Rzycki
Departmental Technical Reports (CS)
To cover a certain area, it is often necessary to combine several satellite photos. To get a proper combination, we need to appropriately position and orient these photos relative to one another, i.e., mosaic these photos. With the new generation of multispectral satellites, for each area, we have several hundred images which correspond to different wavelengths. At present, when we mosaic two images, we only use one of the wavelengths and ignore the information from the other wavelengths. It is reasonable to decrease the mosaicking error by using images corresponding to all possible wavelengths in mosaicking. In this paper ...
Fundamental Properties Of PairWise Interactions Naturally Lead To Quarks And Quark Confinement: A Theorem Motivated By Neural Universal Approximation Results, Vladik Kreinovich
Fundamental Properties Of PairWise Interactions Naturally Lead To Quarks And Quark Confinement: A Theorem Motivated By Neural Universal Approximation Results, Vladik Kreinovich
Departmental Technical Reports (CS)
In traditional mechanics, most interactions are pairwise; if we omit one of the particles from our description, then the original pairwise interaction can sometimes only be represented as interaction between triples, etc. It turns out that, vice versa, every possible interaction between N particles can be represented as pairwise interaction if we represent each of the original N particles as a triple of new ones (and two new ones are not enough for this representation). The resulting three "particles" actually represent a single directly observable particles and in this sense, cannot be separated. So, this representation gives a fundamental reason ...
On Granularity In Fuzzy Logic: Minimum And Maximum Are The Only Absolutely Granular TNorm And TConorm, Vladik Kreinovich, Bernadette BouchonMeunier
On Granularity In Fuzzy Logic: Minimum And Maximum Are The Only Absolutely Granular TNorm And TConorm, Vladik Kreinovich, Bernadette BouchonMeunier
Departmental Technical Reports (CS)
No abstract provided.