- Special Issue on the Linkages Between Interval Mathematics and Fuzzy Set Theory
- Special Issue on Dependable Reasoning about Uncertainty, also in PostScript and in pdf
- Special Issue on Applications to Control, Signals, and Systems
- Special Issue on Reliable Geometric Computations
- Student Issues

Reliable Computing will devote a special issue to papers that address the interrelationship between interval mathematics and fuzzy set theory. The connection between interval mathematics and fuzzy set theory is evident in the extension principle, arithmetic, logic, and in the mathematics of uncertainty. Much of the research to date has been in the use of interval mathematics in fuzzy set theory, in particular fuzzy arithmetic and fuzzy interval analysis. This may be because intervals can be considered as a particular type of fuzzy set. The impact of fuzzy set theory on interval mathematics is not quite as evident. For example, it is clear that fuzzy logic, fuzzy control, fuzzy neural networks, and fuzzy cluster analysis, are four important areas of fuzzy set theory. The impact of interval analysis on these four areas is not as apparent. Can the development in these areas of fuzzy set theory inform research in interval mathematics?

There are areas of interval mathematics and fuzzy set theory that have developed in parallel with little or no interchange of ideas. In particular the extension principle of Zadeh and the united extension of R.E. Moore as well as subsequent research in this area has largely been developed independently. Both are related to set-valued functions. Is there a useful underlying unifying mathematics? Secondly, dependencies and their effect on the resulting arithmetic has more recently been a part of the fuzzy set theory literature and approaches independently developed from what has been known in the interval analysis community almost since the beginnings of interval analysis research. Are there other areas of interval analysis research that would be useful for the fuzzy set theory community to know about?

One of the paths of interval mathematics research has led to validation analysis. Is there a useful comparable counterpart for fuzzy set theory? Interval analysis is the way to model the uncertainty arising from computer computations. Thus, interval analysis shares mathematical uncertainty modeling with the field of fuzzy set theory. So, fundamentally, what are the common points between interval analysis and fuzzy set theory? In interval analysis, convergence of algorithms has been an area of research. Are there extensions of these approaches to fuzzy algorithms? In the area of interval analysis, much work has been done in validation methods for differential equations. A few research papers have appeared in this area in the fuzzy set theory setting. Are there areas of cross-fertilization? There are many research papers in the area of optimization in both interval analysis and fuzzy set theory. What is the interrelationship between interval and fuzzy optimization? Is there a fundamental mathematical foundation out of which both arise?

The following lists a few areas of interest. It is indicative and not exhaustive.

- Fuzzy and interval mathematical analysis
- Comparative analysis of the interval and fuzzy logics
- Upper and lower dependency bounds in interval and fuzzy mathematics
- Dependency analysis in interval and fuzzy computations
- Fuzzy and interval methods in classification (cluster) analysis
- The use of fuzzy set theory and interval analysis methods in neural networks
- Interval and fuzzy ordering methods
- The use of interval analysis and fuzzy set theory in neural networks
- The use of interval analysis and fuzzy set theory in surface modeling, interpolation and approximation
- The application of interval analysis to fuzzy algorithms and vice versa
- The methods and relationship between interval and fuzzy optimization
- Fuzzy and interval logic controllers
- Computer systems in support of fuzzy number data types and associated numerical algorithms akin to such interval analysis computer systems as that of S.Rump, INTLAB-Interval Laboratory
- Interval and fuzzy methods for differential equations
- Convergence and complexity analysis of interval and fuzzy algorithms
- One of the uses of interval analysis is in the validation of solutions under computational and data errors. Is there a comparable use of fuzzy set and possibility theory in the validation of solutions under uncertainty?

Professor Weldon A. Lodwick

Department of Mathematics-Campus Box 170

University of Colorado at Denver

P.O. Box 173364

Denver, Colorado 80217--3364

weldon.lodwick@cudenver.edu

Telephone: +1 303 556-8462

Schedule:

October 15, 2002: Deadline for submission of papers to the special issue.

April 15, 2002: Notification about acceptance of papers.

July 15, 2003: Revisions to accepted papers due.

Manuscripts will be subjected to the usual reviewing process and should conform to the standards and formats as indicated in the "Information for Authors" section inside the back cover of Reliable Computing. Contributions should not exceed 32 pages.

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Reliable Computing will devote a special issue to papers in the area of reliable geometric computations.

Interest in geometric computations is steadily increasing in a number of fields such as computer graphics, solid modeling, geographic information systems, astrophysics, and civil engineering to mention a few. Additionally computational geometry is a field entirely devoted to geometric computations.

Within the field of computational geometry a number of geometric algorithms have been developed that are optimal with respect to the order of the problem size. These algorithms normally require exact (that is real) arithmetic for their correct implementation.

When the geometric algorithms are implemented on a computer using floating-point arithmetic then they might fail to give correct results. A number of approaches to remedy this situation have been tried such as infinite arithmetic, variable precision arithmetic, precise rational arithmetic, perturbation approaches, epsilon-arithmetic etc.

The special problems that arise with respect to computer implementations of geometric computations can often be attributed to the tight coupling between numerical computations and logical decision making. Because of this, small perturbations in numerically computed results may cause large changes in program execution flow. For an example from computer graphics consider a ray-tracing program. A ray passing close to an object will follow a path that is quite different from a ray intersecting an object. Small perturbations of the ray will send it along the one or the other path. Another problem is how to handle degeneracies. Consider a plane in 3D. It is defined by three points, yet many objects in, for example, solid geometry have rectangular or polygonal faces which means that the set of points defining the faces overdetermine the faces.

The problems mentioned above are of great interest in the application fields mentioned above. Programs involving geometric computations tend to work well for many case, but fail for a small but significant number of cases. The reasons for failure is also often not well understood. These failures are unacceptable in commercial software.

The special issue will be devoted to papers proposing reliable and applicable methods for geometric computations.

March 1, 1998: deadline for submission of papers for the special issue.

Sept. 1998: Authors will be informed about acceptance of papers.

Dec. 1, 1998: Revisions to accepted papers due.

Addresses for submissions:

Helmut Ratschek

Mathematisches Institut

der Universitat

D-40225 Dusseldorf

Germany

E-mail
ratschek@math.uni-duesseldorf.de

Jon Rokne

Department of Computer Science

University of Calgary

Calgary, Alberta

Canada T2N-1N4

E-mail rokne@cpsc.ucalgary.ca

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Besides these data uncertainties, the designer is faced with another difficulty: Many problems require a yes/no answer, e.g., stable/unstable. Even when an algorithm designed to solve such a problem can find the correct result using real arithmetic, it may fail to do so due to rounding errors when implemented on a computer using floating point arithmetic.

Interval methods appear as an appropriate tool to cope with data uncertainties as well as with rounding errors. However, designers are often confronted with a nonlinear uncertainty structure which makes the problem considerably more difficult. E.g., after massaging the study of the stability of some uncertain system into a polynomial problem with coefficients depending on uncertain parameters, these parameters generally enter into more than one coefficient of the polynomial, and in many cases, these coefficients depend nonlinearly on the uncertain parameters. In addition to the traditional domain of affine and multiaffine uncertainty structure, recent advances have opened up potential new application areas for reliable methods in communications, control, signal processing, and related fields.

The application-oriented special issue of Reliable Computing is intended to provide a forum for the presentation of advances in using reliable methods in these areas.

Contributions for this special issue should be sent as LaTeX file and as hard copy to both of the following Guest Editors before July 31, 1998:

Juergen Garloff

Fachhochschule Konstanz

Fachbereich Informatik

Postfach 10 05 43

D--78405 Konstanz

Germany

Tel.: +49-7531-206-627 or -597

Fax: +49-7531-206-559

email garloff@fh-konstanz.de

and

Eric Walter

Laboratoire des Signaux et Systemes

CNRS--Ecole Superieure d' Electricite

F--91192 Gif-sur-Yvette Cedex

Tel.: +33-1-69-85-17-21

Fax: +33-1-69-41-30-60

email walter@lss.supelec.fr

Manuscripts will be subjected to the usual reviewing process and should conform to the standard formats as indicated in the "Aims and Scope" Section inside the back cover of Reliable Computing (see). Contributions should not exceed 32 pages.

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Reliable Computing

We will try our best to publish these issues as fast as possible. Papers should be (ideally) written in a version of TeX (preferably plain LaTeX or plain TeX).

Please submit your papers to one of the editors:

Vladik Kreinovich

Department of Computer Science

University of Texas at El Paso

El Paso, TX 79968, USA

phone (915) 747-6951

fax (915) 747-5030

email vladik@utep.edu

Guenter Mayer

Fachbereich Mathematik

Universitaet Rostock

Universitaetsplatz 1

D-18051 Rostock, Germany

office ++ (381) 498-1553

fax ++ (381) 498-1520

email guenter.mayer@mathematik.uni-rostock.de

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