## University of Texas at El Paso Computer Science Department Abstracts of 1998 Reports

Technical Report UTEP-CS-98-35, December 1998
Towards Intelligent Virtual Environment for Teaching Telemanipulation Operators: Virtual Tool Approach and its Interval-Based Justification
L. Olac Fuentes and Vladik Kreinovich

Published in: Proceedings of the Second International Workshop on Intelligent Virtual Environments, Xalapa, Veracruz, Mexico, September 11-12, 1998, pp. 8-11.

Technical Report UTEP-CS-98-34, December 1998
Interval Image Classification is NP-Hard
Alejandro E. Brito and Vladik Kreinovich

Published in: Proceedings of the Second International Workshop on Intelligent Virtual Environments, Xalapa, Veracruz, Mexico, September 11-12, 1998, pp. 12-15.

Feature extraction from images to perform object classification is a very hard problem for general solution. We prove that under interval uncertainty, linear classification is NP-hard.

Technical Report UTEP-CS-98-33, December 1998
Towards Optimal Pain Relief: Acupuncture and Spinal Cord Stimulation
Richard Alo, Kenneth Alo, Obinna Ilochonwu, Vladik Kreinovich, and Hoang Phuong Nguyen

Published in: Proceedings of the Second International Workshop on Intelligent Virtual Environments, Xalapa, Veracruz, Mexico, September 11-12, 1998, pp. 16-24.

One of the important potential areas of application of intelligent virtual environment is to training medical doctors. One of the main problems in designing the corresponding intelligent system is the computational complexity of the corresponding computational problems. This computational complexity is especially high when the corresponding optimization is a discrete optimization problem, e.g., for pain relief methodologies such as acupuncture and spinal cord stimulation. In this paper, we show how to efficiently solve the corresponding discrete optimization problems. As a result, we get, e.g., a theoretical justification for the heuristic method of "guarded cathode".

Technical Report UTEP-CS-98-32, December 1998
Interval Computations, Soft Computing, and Aerospace Applications
Vladik Kreinovich

Published in: Proceedings of the Second International Workshop on Intelligent Virtual Environments, Xalapa, Veracruz, Mexico, September 11-12, 1998, pp. 25-41.

Technical Report UTEP-CS-98-31, December 1998
Justification of Heuristic Methods in Data Processing Using Fuzzy Theory, with Applications to Detection of Business Cycles from Fuzzy Data
Vladik Kreinovich, Hung T. Nguyen, and Berlin Wu

Published in Proceedings of FUZZ-IEEE'99, Seoul, Korea, August 22-25, 1999, Vol. 2, pp. 1131-1136. Full version published in East-West Journal of Mathematics, 1999, Vol. 1, No. 2, pp. 147-157.

In this paper, we show that fuzzy theory can explain heuristic methods in inverse problems and numerical computations. As an example of application of these results, we analyze the problem of detecting business cycles from fuzzy data.

Technical Report UTEP-CS-98-30, October 1998
Towards Foundations for Traditional Oriental Medicine
Hoang Phuong Nguyen, Scott A. Starks, and Vladik Kreinovich

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 704-708.

Technical Report UTEP-CS-98-29, September 1998
NP-Hardness in Geometric Construction Problems with One Interval Parameter
Nuria Mata and Vladik Kreinovich

Published as Universitat Politecnica de Catalunya, Departament de Llenguatges i Sistemes Informatics Barcelona, Spain, Technical Report No. LSI-98-55-R, November 1998; final version appeared in: Proceedings of the Workshop on Applications of Interval Analysis to Systems and Control with special emphasis on recent advances in Modal Interval Analysis MISC'99, Girona, Spain, February 24-26, 1999, pp. 85-98.

Technical Report UTEP-CS-98-28, September 1998
Fuzzy Justification of Heuristic Methods in Inverse Problems and in Numerical Computations, with Applications to Detection of Business Cycles from Fuzzy and Intuitionistic Fuzzy Data
Vladik Kreinovich, Hung T. Nguyen, Berlin Wu, and Krassimir T. Atanassov

Published in Notes on Intuitionistic Fuzzy Sets (NIFS), 1998, Vol. 4, No. 2, pp. 47-56.

Technical Report UTEP-CS-98-27, August 1998
From Semi-Heuristic Fuzzy Techniques to Optimal Fuzzy Methods: Mathematical Foundations and Applications
Vladik Kreinovich

In: Basil Papadopoulos and Apostolos Syropoulos (eds.), Current Trends and Developments in Fuzzy Logic, Proceedings of the First International Workshop, Thessaloniki, Greece, October 16-20, 1998, pp. 1-62.

Fuzzy techniques have been successfully used in various application areas ranging from control to image processing to decision making. In all these applications, there is usually:

• a general idea, and then
• there are several possible implementations of this idea; e.g., we can use:
• different membership functions,
• different "and" and "or" operations,
• different defuzzifications, etc.
In the first approximation, the results are usually reasonably robust and independent on this choice, so any heuristic or semi-heuristic choice works OK. However:
• if we want to further improve the semi-heuristic "good enough" control or image processing techniques,
• we must actually make the selection that would lead to an optimal fuzzy method.

Even if we know the exact optimality criterion, the resulting optimization problem is so complicatedly non-linear that, often, no known optimization techniques can be used. In many real-life situations, we do not even know the exact criterion: the relative quality of different controls or image processing techniques may be not by exact numerical criteria, but rather by expert opinions which are, themselves, fuzzy.

In this talk, we describe a general mathematical technique for solving such optimization problems. This technique is based on the group-theoretic (symmetry) methodology, a methodology which is one of the main successful tools of modern physics. This methodology has lead us to the justification of many heuristic formulas in fuzzy logic, fuzzy control, neural networks, etc. (many examples are presented in our 1997 Kluwer book with H.T. Nguyen "Applications of continuous mathematics to computer science").

We also present new applications of this techniques, including applications:

• to optimal fuzzy control, and
• to optimal fuzzy image processing.

Technical Report UTEP-CS-98-26, August 1998
Towards Combining Fuzzy and Logic Programming Techniques
Hung T. Nguyen, Vladik Kreinovich, Daniel E. Cooke, Luqi, and Olga Kosheleva

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 482-489.

Technical Report UTEP-CS-98-25, August 1998
Towards Formalization of Feasibility, Randomness, and Commonsense Implication: Kolmogorov Complexity, and the Necessity of Considering (Fuzzy) Degrees
Vladik Kreinovich, Luc Longpre, and Hung T. Nguyen

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 294-302.

Technical Report UTEP-CS-98-24, August 1998
Cooperative Learning is Better: Explanation Using Dynamical Systems, Fuzzy Logic, and Geometric Symmetries
Vladik Kreinovich, Edye Johnson-Holubec, Leonid K. Reznik, and Misha Koshelev

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 154-160.

Technical Report UTEP-CS-98-23, August 1998
How to Describe Partially Ordered Preferences: Mathematical Foundations
Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen, and Bernadette Bouchon-Meunier

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 269-278.

Technical Report UTEP-CS-98-22, August 1998
Uncertainty Representation Explains and Helps Methodology of Physics and Science in General
Misha Koshelev, Vladik Kreinovich, Hung T. Nguyen, and Bernadette Bouchon-Meunier

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 577-585.

Technical Report UTEP-CS-98-21, August 1998
Complex Problems: Granularity is Necessary, Granularity Helps
Oscar N. Garcia, Vladik Kreinovich, Luc Longpre, and Hung T. Nguyen

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 449-455.

Technical Report UTEP-CS-98-20, August 1998
Possible New Directions in Mathematical Foundations of Fuzzy Technology: A Contribution to the Mathematics of Fuzzy Theory
Hung T. Nguyen and Vladik Kreinovich

In: Nguyen Hoang Phuong and Ario Ohsato (eds.), Proceedings of the Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September-2nd October, 1998, pp. 9-32.

Technical Report UTEP-CS-98-19, July 1998
Updated version UTEP-98-19a, June 1999
Final version UTEP-98-19b, October 1999
Interval Methods in Non-Destructive Testing of Material Structures
Keith Worden, Roberto Osegueda, Carlos Ferregut, Soheil Nazarian, Debra L. George, Mary J. George, and Vladik Kreinovich, Olga Kosheleva and Sergio Cabrera

Published in Reliable Computing, 2001, Vol. 7, No. 4, pp. 341-352.

In many practical situations, e.g., in aerospace applications and in mammography, it is important to test the structural integrity of material structures. We show that interval methods can help.

Postscript file of the first version;
Compressed Postscript file of the updated version;
Final version UTEP-98=19b in Compressed Postscript and in pdf

Technical Report UTEP-CS-98-18, July 1998
Beyond Interval Systems: What is Feasible and What is Algorithmically Solvable?
Vladik Kreinovich

Published in: Panos M. Pardalos (ed.), Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, Kluwer, Dordrecht, 1999, pp. 364-379.

In many real-life applications of interval computations, the desired quantities appear (in a good approximation to reality) as a solution to a system of interval linear equations. It is known that such systems are difficult to solve (NP-hard) but still algorithmically solvable. If instead of the (approximate) interval linear systems, we consider more realistic (and more general) formulations, will the corresponding problems still be algorithmically solvable? We consider three natural generalizations of interval linear systems: to conditions which are more general than linear systems, to multi-intervals instead of intervals, and to dynamics (differential and difference equations) instead of statics (linear and algebraic equations). We show that the problem is still algorithmically solvable for non-linear systems and even for more general conditions, and it is still solvable if we consider linear or non-linear systems with multi-intervals instead of intervals. However, generalized conditions with multi-interval uncertainty are already algorithmically unsolvable. For dynamics: difference equations are still algorithmically solvable, differential equations are, in general, unsolvable.

Technical Report UTEP-CS-98-17, June 1998
A Simplified Version of the Tomography Problem Can Help to Estimate the Errors of Indirect Measurements
V. Kreinovich

In: Ali Mohamad-Djafari (ed.), Bayesian Inference for Inverse Problems, Proceedings of the SPIE/International Society for Optical Engineering, Vol. 3459, San Diego, CA, 1998, pp. 106-115.

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, we show that in a natural statistical setting, the problem of estimating the error of indirect measurement can be formulated as a simplified (finite-dimensional) version of a tomography problem (reconstructing an image from its projections).

In this paper, we use the ideas of invariance (natural in statistical setting) to find the optimal algorithm for solving this simplified tomography problem, and thus, for solving the statistical problem of error estimation for indirect measurements.

Technical Report UTEP-CS-98-16, June 1998
Multi-Spectral Inverse Problems in Satellite Image Processing
S. A. Starks and V. Kreinovich

In: Ali Mohamad-Djafari (ed.), Bayesian Inference for Inverse Problems, Proceedings of the SPIE/International Society for Optical Engineering, Vol. 3459, San Diego, CA, 1998, pp. 138-146.

Satellite imaging is nowadays one of the main sources of geophysical and environmental information. It is, therefore, extremely important to be able to solve the corresponding inverse problem: reconstruct the actual geophysics- or environment-related image from the observed noisy data.

Traditional image reconstruction techniques have been developed for the case when we have a single observed image. This case corresponds to a single satellite photo. Existing satellites (e.g., Landsat) take photos in several (up to 7) wavelengths. To process this multiple-spectral information, we can use known reasonable multi-image modifications of the existing single-image reconstructing techniques. These modifications, basically, handle each image separately, and try to merge the resulting information.

Currently, a new generation of imaging satellites (Lewis) is being launched, that will enable us to collect visual images for about 500 different wavelengths. This two order of magnitude increase in data amount should lead to a similar increase in the processing time, but surprisingly, it does not. An analysis and explanation of this paradoxical simplicity is given in the paper.

Technical Report UTEP-CS-98-15, June 1998
Case Study of Non-Linear Inverse Problems: Mammography and Non-Destructive Evaluation
O. Kosheleva, S. Cabrera, R. Osegueda, C. Ferregut, S. Nazarian, D. L. George, M. J. George, V. Kreinovich, and K. Worden

In: Ali Mohamad-Djafari (ed.), Bayesian Inference for Inverse Problems, Proceedings of the SPIE/International Society for Optical Engineering, Vol. 3459, San Diego, CA, 1998, pp. 128-135.

The inverse problem is usually difficult because the signal (image) that we want to reconstruct is weak. Since it is weak, we can usually neglect quadratic and higher order terms, and consider the problem to be linear. Since the problem is linear, methods of solving this problem are also, mainly, linear (with the notable exception of the necessity to take into consideration, e.g., that the actual image is non-negative).

In most real-life problems, this linear description works pretty well. However, at some point, when we start looking for a better accuracy, we must take into consideration non-linear terms. This may be a minor improvement for normal image processing, but these non-linear terms may lead to a major improvement and a great enhancement if we are interested in outliers such as faults in non-destructive evaluation or bumps in mammography. Non-linear terms (quadratic or cubic) give a great relative push to large outliers, and thus, in these non-linear terms, the effect of irregularities dominate. The presence of the non-linear terms can serve, therefore, as a good indication of the presence of irregularities.

We describe the result of the experiments in which these non-linear terms are really helpful.

Technical Report UTEP-CS-98-14, June 1998
Kolmogorov Complexity, Statistical Regularization of Inverse Problems, and Birkhoff's Formalization Of Beauty
V. Kreinovich, L. Longpre, and M. Koshelev

In: Ali Mohamad-Djafari (ed.), Bayesian Inference for Inverse Problems, Proceedings of the SPIE/International Society for Optical Engineering, Vol. 3459, San Diego, CA, 1998, pp. 159-170.

Most practical applications of statistical methods are based on the implicit assumption that if an event has a very small probability, then it cannot occur. For example, the probability that a kettle placed on a cold stove would start boiling by itself is not 0, it is positive, but it is so small, that physicists conclude that such an event is simply impossible.

This assumption is difficult to formalize in traditional probability theory, because this theory only describes measures on sets (e.g., for an inverse problem, on the set of all functions) and does not allow us to divide functions into "random" (possible) and non-random ("impossible") ones. This distinction was made possible by the idea of algorithmic randomness, introduced by Kolmogorov and his student Martin-Lof in the 1960s.

We show that this idea can also be used for inverse problems. In particular, we prove that for every probability measure, the corresponding set of random functions is compact, and, therefore, the correspondingly restricted inverse problem is well-defined.

The resulting techniques turns out to be interestingly related with the qualitative esthetic measure introduced by G. Birkhoff as order/complexity.

Technical Report UTEP-CS-98-13, May 1998
Updated version UTEP-CS-98-13a, June 1998
Fair Division under Interval Uncertainty
Ronald R. Yager and Vladik Kreinovich

Published in International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems (IJUFKS), 2000, Vol. 8, No. 5, pp. 611-618.

It is often necessary to divide a certain amount of money between n participants, i.e., to assign, to each participant, a certain portion w(i)>=0 of the whole sum (so that w(1)+...+w(n)=1). In some situations, from the fairness requirements, we can uniquely determine these "weights" w(i). However, in some other situations, general considerations do not allow us to uniquely determine these weights, we only know the intervals [w-(i),w+(i)] of possible fair weights. We show that natural fairness requirements enable us to choose unique weights from these intervals; as a result, we present an algorithm for fair division under interval uncertainty.

Postscript file of the original paper;
Updated version in Compression Postscript and pdf.

Technical Report UTEP-CS-98-12, May 1998
Updated version UTEP-CS-98-12a, June 1999
Decision Making under Interval Probabilities
Ronald R. Yager and Vladik Kreinovich

Published in International Journal of Appeoximate Reasoning, Vol. 22, No. 3, pp. 195-215.

If we know the probabilities p(1),...,p(n) of different situations s1,...,sn, then we can choose a decision Ai for which the expected benefit C(i)=p(1)*c(i,1)+...+p(n)*c(i,n) takes the largest possible value, where c(i,j) denotes the benefit of decision Ai in situation sj. In many real life situations, however, we do not know the exact values of the probabilities p(j); we only know the intervals [p-(j),p+(j)] of possible values of these probabilities. In order to make decisions under such interval probabilities, we would like to generalize the notion of expected benefits to interval probabilities. In this paper, we show that natural requirements lead to a unique (and easily computable) generalization. Thus, we have a natural way of decision making under interval probabilities.

Postscript file of the first version;
Updated version in Compressed Postscript and in pdf.

Technical Report UTEP-CS-98-11, March 1998
Towards the Use of Aesthetics in Decision Making: Kolmogorov Complexity Formalizes Birkhoff's Idea
Misha Koshelev, Vladik Kreinovich, and Yeung Yam

Decision making is traditionally based on utilitarian criteria such as cost, efficiency, time, etc. These criteria are reasonably easy to formalize; hence, for such criteria, we can select the best decision by solving the corresponding well-defined optimization problem. In many engineering projects, however, e.g., in designing cars, building, airplanes, etc., an important additional criterion which needs to be satisfied is that the designed object should be good looking. This additional criterion is difficult to formalize and, because of that, it is rarely taken into consideration in formal decision making. In the 1930s, the famous mathematician G. D. Birkhoff has proposed a formula that described beauty in terms of "order" and "complexity". In the simplest cases, he formalized these notions and showed that his formula is indeed working. However, since there was no general notion of complexity, he was unable to formalize his idea in the general case. In this paper, we show that the existing computer-based general notion of object complexity (called Kolmogorov complexity) leads to a reasonable formalization of Birkhoff's idea and thus, leads to a possibility to take aesthetic criteria into consideration in decision making.

Technical Report UTEP-CS-98-10, February 1998
An Operationalistic Reformulation of Einstein's Equivalence Principle
V. Ya. Kreinovich and R. R. Zapatrine

Published in Gravitacija, 1997, Vol. 3, No. 2, pp. 51-59 (in Russian).

Technical Report UTEP-CS-98-9, February 1998
Encryption Algorithms Made (Somewhat) More Natural (A Pedagogical Remark)
Misha Koshelev, Vladik Kreinovich, and Luc Longpre

Short version published in Bulletin of the European Association for Theoretical Computer Science (EATCS), 1999, Vol. 67, pp. 153-156; full version published in Inroads: ACM SIGCSE Bulletin, 1999, Vol. 31, No. 4, pp. 50-51.

Modern cryptographic algorithms, such as DES, IDEA, etc., are very complex and therefore difficult to learn. Textbooks explain in detail how these algorithms work, but they usually do not explain why these algorithms were designed as they were. In this paper, we explain why, and thus, hopefully, make cryptographic algorithms easier to learn.

Technical Report UTEP-CS-98-8, January 1998
Application of Kolmogorov Complexity to Image Compression: It is Possible to Have a Better Compression, but It is Not Possible to Have the Best One
Sanjeev Subbaramu, Ann Q. Gates, and Vladik Kreinovich

Published in Bulletin of the European Association for Theoretical Computer Science (EATCS), 1999, Vol. 69, pp. 145-150.

Technical Report UTEP-CS-98-7, January 1998
Telemanipulation: The Virtual Tool Approach and its Interval-Based Justification
Vladik Kreinovich and Luic Olac Fuentes

In: Goetz Alefeld and Raul A. Trejo (eds.), Interval Computations and its Applications to Reasoning Under Uncertainty, Knowledge Representation, and Control Theory. Proceedings of MEXICON'98, Workshop on Interval Computations, 4th World Congress on Expert Systems, Mexico City, Mexico, 1998.

Technical Report UTEP-CS-98-6, January 1998
Run-Time Correctness Checking is Algorithmically Undecidable for Pointer Data Structures
Mikhail Auguston, Vladik Kreinovich, and Luc Longpre

Programs routinely use complicated pointer (linked list-type) data structures such as linked lists, doubly linked lists, different types of trees, etc. These data structures are usually defined {\it inductively}: e.g., a tree can be defined as a structure that results from an empty tree by an arbitrary sequence of adding and deleting elements.

When the program runs, these data structures take dynamically changing shapes. To test program correctness, it is important to check, at run-time, whether a current shape is a correct implementation of the corresponding structure. Algorithms are known for checking the shape correctness'' for basic pointer-based data structures such as linked list, binary tree, etc.

In this paper, we show that the general problem - verifying that a given shape is an instance of an inductively defined data structure - is algorithmically undecidable.

Technical Report UTEP-CS-98-5, January 1998
Ordinal Explanation of the Periodic System of Chemical Elements
Eric R. Scerri, Vladik Kreinovich, Piotr Wojciechowski, and Ronald R. Yager

Published in the International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems (IJUFKS), 1998, Vol. 6, No. 4, pp. 387-399.

Textbooks often claim that quantum mechanics explained the periodic system: namely, the actual configuration of electronic orbits that is responsible for the element's chemical properties can be described as the one that minimizes the total energy, and the energy of each configuration can be computed by using quantum mechanics.

However, a careful analysis of this explanation reveals that, in addition to the basic equations of quantum mechanics, we need some heuristic rules that do not directly follow from quantum physics. One reason why additional heuristics are necessary is that the corresponding numerical equations are extremely difficult to solve, and as we move to atoms with larger and larger atomic numbers Z, they become even more difficult. Moreover, as Z grows, we must take relativistic effects into consideration, and this means going from partial differential equations to even more mathematically difficult operator equations.

In this paper, we show that if instead of the (often impossible) numerical optimization, we consider the (available) ordinal information, we can then explain the observed periodic system.

Technical Report UTEP-CS-98-4, January 1998
Human Visual Perception and Kolmogorov Complexity: Revisited
Vladik Kreinovich and Luc Longpre

Published in the Bulletin of the European Association for Theoretical Computer Science (EATCS), 1998, Vol. 64, pp. 155-158.

Experiments have shown that we can only memorize images up to a certain complexity level, after which, instead of memorizing the image itself, we, sort of, memorize a probability distribution in terms of which this image is "random" (in the intuitive sense of this word), and next time, we reproduce a "random" sample from this distribution. This random sample may be different from the original image, but since it belongs to the same distribution, it, hopefully, correctly reproduces the statistical characteristics of the original image.

The reason why a complex image cannot be accurately memorized is, probably, that our memory is limited. If storing the image itself exhausts this memory, we store its probability distribution instead. With this limitation in mind, we conclude that we cannot store arbitrary probability distributions either, only sufficient simple ones.

In this paper, we show that an arbitrary image is indeed either itself simple, or it can be generated by a simple probability distribution. This result provides a mathematical foundations for the above theoretical explanation of the randomized-memorization phenomena.

File in Postscript and in pdf.

Technical Report UTEP-CS-98-3, January 1998
On Geometry of Radio Antenna Placements
Olga Kosheleva, Vladik Kreinovich, Andrei M. Finkelstein, and Steven Chan

Published in Geombinatorics, 1998, Vol. 8, No. 2, pp. 46-49.

Technical Report UTEP-CS-98-2b, March 1998
Decision Making Based on Satellite Images: Optimal Fuzzy Clustering Approach
Vladik Kreinovich, Hung T. Nguyen, Scott A. Starks, and Yeung Yam

Published in Proceedings of the 37th IEEE Conference on Decision and Control CDC'98, Tampa, Florida, December 16-18, 1998, pp. 4246-4251.

In many real-life decision-making situations, in particular, in processing satellite images, we have an enormous amount of information to process. To speed up the information processing, it is reasonable to first classify the situations into a few meaningful classes (clusters), find the best decision for each class, and then, for each new situation, to apply the decision which is the best for the corresponding class. One of the most efficiently clustering methodologies is fuzzy clustering, which is based on the use of fuzzy logic. Usually, heuristic clusterings are used, i.e., methods which are selected based on their empirical efficiency rather than on their proven optimality. Because of the importance of the corresponding decision making situations, it is therefore desirable to theoretically analyze these empirical choices. In this paper, we formulate the problem of choosing the optimal fuzzy clustering as a precise mathematical problem, and we show that in the simplest cases, the empirically best fuzzy clustering methods are indeed optimal.

Technical Report UTEP-CS-98-2, January 1998
Optimal Choices of Potential Functions in Fuzzy Clustering
Vladik Kreinovich, Hung T. Nguyen, and Yeung Yam

Published by The Chinese University of Hong Kong, Department of Mechanical and Automation Engineering, as Technical Report CUHK-MAE-98-001, January 1998.

Fuzzy logic-based clustering techniques are widely used in situations where statistical assumptions are not valid. Whether in estimating cluster centers for model identification purposes or in determining clusters the existing techniques are essentially based upon the choice of some potential functions. As in any design problems of this kind, the choice of such a function has to be justified on a theoretical basis. In this work, we set up a decision frame work and show that optimal potential functions are the ones which are used in current techniques.

Technical Report UTEP-CS-98-1, January 1998
On How to Merge Sorted Lists Coming from Different Web Search Tools
Ronald R. Yager and Vladik Kreinovich

Published in Soft Computing, 1999, Vol. 3, pp. 83-88.

Different web search tools often complement each other. So, if we want to have a good coverage of all relevant web items, a reasonable strategy is to use different search tools and then merge the resulting lists. How to merge them? In this paper, we describe reasonable axioms for the merging procedure and describe all mergings that satisfy these reasonable axioms.