Computer Engineering Commons^™

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 …

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

Departmental Technical Reports (CS)

No abstract provided.

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 …

Which Truth Values In Fuzzy Logics Are Definable?, Hung T. Nguyen, Vladik Kreinovich, Antonio Di Nola

Departmental Technical Reports (CS)

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0,1]. There are only denumerable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathematical terms, which real numbers are definable in the corresponding fuzzy logic.

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 …

Interval Computations As A Particular Case Of A General Scheme Involving Classes Of Probability Distributions, Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Harry Schulte

Departmental Technical Reports (CS)

Traditionally, in science and engineering, measurement uncertainty is characterized by a probability distribution; however, we don't know this probability distribution exactly, so we must consider classes of probability distributions. Interval computations deal with a very specific type of such classes: classes of all distributions which are located on a given interval. We show that in general, we need all convex classes of probability distributions.

1st Order, 2nd Order, What Next? Do We Really Need Third-Order Descriptions: A View From A Realistic (Granular) Viewpoint, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

To describe experts' uncertainty in a knowledge-based system, we usually use numbers from the interval [0,1] (subjective probabilities, degrees of certainty, etc.). The most direct way to get these numbers is to ask the expert; however, the expert may not be 100\% certain what exactly number describes his uncertainty; so, we end up with a second-order uncertainty - a degree of certainty describing to what extent a given number d adequately describes the expert's uncertainty about a given statement A. At first glance, it looks like we should not stop at this second order: the expert is probably as uncertain …

Computing The Shape Of The Image Of A Multi-Linear Mapping Is Possible But Computationally Intractable: Theorems, Raul A. Trejo, Vladik Kreinovich

Departmental Technical Reports (CS)

In systems without inertia (or with negligible inertia), a change in the values of control variables x1,...,xn leads to the immediate change in the state z of the system. In more precise terms, for such systems, every component zi of the state vector z=(z1,...,zd) is a function of the control variables. When we know what state z we want to achieve, the natural question is: can we achieve this state, i.e., are there values of the control variables which lead to this very state?

The simplest possible functional dependence is described by linear functions. For such functions, the question of …

An Even More Realistic (Non-Associative) Interval Logic And Its Relation To Psychology Of Human Reasoning, I. R. Goodman, Raul Trejo, Vladik Kreinovich, Jesus Martinez, Reginaldo Gonzalez

Departmental Technical Reports (CS)

No abstract provided.

Why Unary And Binary Operations In Logic: General Result Motivated By Interval-Valued Logics, Hung T. Nguyen, Vladik Kreinovich, I. R. Goodman

Departmental Technical Reports (CS)

Traditionally, in logic, only unary and binary operations are used as basic ones - e.g., "not", "and", "or" - while the only ternary (and higher order) operations are the operations which come from a combination of unary and binary ones. For the classical logic, with the binary set of truth values {0,1}, the possibility to express an arbitrary operation in terms of unary and binary ones is well known: it follows, e.g., from the well known possibility to express an arbitrary operation in DNF form. A similar representation result for [0,1]-based logic was proven in our previous paper. In this …

How To Make Sure That "~100" + 1 Is ~100 In Fuzzy Arithmetic: Solution And Its (Inevitable) Drawbacks, Vladik Kreinovich, Hung T. Nguyen, Witold Pedrycz

Departmental Technical Reports (CS)

From the commonsense viewpoint, if a person who weighs around 100 kilograms gains one more kilogram, his weight is still around 100 kilograms. Alas, not so in traditional fuzzy arithmetic. In this paper, we propose a modification of fuzzy arithmetic which does have this property. We gain the desired property, but there is no free lunch, we have to lose two important properties of the traditional fuzzy arithmetic: first, addition is no longer always associative; second, addition is no longer always easily computable.

What Is The Best Way To Draw A Cube? A Hypercube?, Brian D'Auriol, Vladik Kreinovich, Bindu George, Florence Muganda, Pramod Kumar Chikkpaiah

Departmental Technical Reports (CS)

One of the possible connections between processors is a hypercube. The simplest case of a hypercube - a 4-vertex square - can be naturally represented on a 2-D page. To represent a 3-dimensional (or higher-dimensional) hypercube, we must project additional dimensions onto a 2-D page. In general, when we project a multi-D space into a 2-D plane, different points project into the same one. To get the best visualization, we must select a projection in such a way that the projections of different points are as distant from each other as possible. In this paper, we formalize and solve the …

On Fusion Of Soft And Hard Computing: Traditional ("Hard Computing") Optimal Rescaling Techniques Simplify Fuzzy Control, Hugh F. Vanlandingham, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main objectives of fuzzy control is to translate expert rules - formulated in imprecise ("fuzzy") words from natural language - into a precise control strategy. This translation is usually done is two steps. First, we apply a fuzzy control methodology to get a rough approximation to the expert's control strategy, and then we tune the resulting fuzzy control system. The first step (getting a rough approximation) is well-analyzed, and the fact that we have expert's intuitive understanding enables us to use soft computing techniques to perform this step. The second (tuning) step is much more difficult: we …

The Prospect For Answer Sets Computation By A Genetic Model, A. Bertoni, G. Grossi, A. Provetti, Vladik Kreinovich, L. Tari

Departmental Technical Reports (CS)

We combine recent results from both Logic Programming and Genetic Algorithms to design a new method for the efficent computation of Answer Sets of logic programs. First of all the problem is reduced to the problem of finding a suitable coloring on directed graphs. Then the problem of finding a suitable coloring is relaxed to a combinatorial optimization problem and solved (in an approximate way) by a continuous discrete time system derived by a genetic model.

Accounting For Domain Context In Evaluation, Meriem Chater, David G. Novick

Departmental Papers (CS)

Work is situated activity. Taking into account human factors in evaluation involves considering not only users but also their contexts of use. Consequently, the evaluation of systems — from video-games to safetycritical interfaces — requires analysis of context to understand not only the effect of context on usability but also the impact of artifacts' usability on users' environments. In the case of safety-critical systems (SCS), errors (by users or designers) may threaten human lives.
To assess the degree to which interface evaluation methods currently account for context, we have used the research strategy taxonomy of McGrath as a framework for …

"Conversational" Dialogues In Direct-Manipulation Interfaces, David G. Novick

Departmental Papers (CS)

This paper reports ongoing research in extending direct-manipulation interfaces by incorporating, via the direct-manipulation modality itself, interaction techniques that add kinds of language features associated with spoken conversation. The paper proposes means of implementing ways for a user of a direct-manipulation system to define new kinds of relations among objects in the interface.

Users And Uses Of Synchronous Business Communications Software, David G. Novick, Eleanor Wynn

Departmental Papers (CS)

To help designers and authors understand users' intentions and work practices for synchronous business communications in a systematic way, we used ethnographic and task-analytic techniques to collect, analyze and classify evidence of the activities of potential users as they conducted their work lives. The interactions we observed among our users took place through a variety of modalities. We found eight categories of tasks for the collaborative or interactive work in which our subjects engaged. Based on these data, we were able to classify roles of potential users of synchronous business communications software into a set of "archetypes" that characterize their …

Itanium's New Basic Operation Of Fused Multiply-Add: Theoretical Explanation And Theoretical Challenge, Vladik Kreinovich

Departmental Technical Reports (CS)

A new Intel's 64-bit chip Itanium has a new instruction set which includes a fused multiply-add 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

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

Departmental Technical Reports (CS)

Smart Dust is a collection of small sensor-equipped 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 3-D locations of all the leaves, and thus, transform their sensor readings into a 3-D 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

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

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 Control-Oriented 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 alpha-cut 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

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 knowledge-based 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 real-time 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 …

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 expected relative size of the informative part of the image.

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 …

Why 95% And Two Sigma? A Theoretical Justification For An Empirical Measurement Practice, Hung T. Nguyen, Vladik Kreinovich, Chin-Wang 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

Departmental Technical Reports (CS)

Several universal approximation and universal representation results are known for non-Boolean multi-valued logics such as fuzzy logics. In this paper, we show that similar results can be proven for multi-valued Boolean logics as well.

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 method-based clustering technique for extraction. A case study is included to demonstrate the effectiveness of the approach.

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.