Mini-track on INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES at the Joint 9th IFSA World Congress and 20th NAFIPS International Conference of NAFIPS, the North American Fuzzy Information Processing Society and IFSA, the International Fuzzy Systems Association IFSA/NAFIPS'01 INTRODUCTION: FUZZY TECHNIQUES In many application areas, we do not have an exact model of the situation and of the objects and processes that we want to analyze and to control. Instead, we have expert knowledge about these objects and processes, knowledge which experts can often only describe by using imprecise ("fuzzy") words and terms from natural languages such as "small", "significant", etc. To enable computers to use this knowledge, it is necessary to reformulate it in computer-understandable terms, and then be able to process thus reformulated knowledge. Techniques for reformulating and processing such "linguistic" (natural-language) knowledge were proposed by Lotfi Zadeh in early 1960's under the name of "fuzzy techniques". In the past decades, these techniques have been successfully used in many application areas, from control to expert systems to medicine. * The success of these techniques is largely due to the fact that from the *methodological* viewpoint, these techniques are based on revolutionary new ideas and approaches, which enabled researchers and engineers to handle problems which could not be solved before. * On the other hand, the practical success of fuzzy techniques is also due to the fact that from the purely *mathematical* and *computational* viewpoint, the corresponding techniques are related to known computational techniques developed and known in non-fuzzy ("crisp") situations. Thus, fuzzy techniques can re-use known algorithms and programs to solve new problems. INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: MAIN RELATION One of the main examples of crisp techniques which are useful in fuzzy applications is interval computations. The reason why interval computations are useful is that the main object of fuzzy techniques - the fuzzy set -- can be viewed as a nested family of sets, or, in 1-D case, the nested family of intervals. These sets (intervals) are called "alpha-cuts" of the original fuzzy set. Many operations with fuzzy sets can be naturally reformulated in terms of the corresponding sets (intervals). Because of this relation, interval methods are widely used in fuzzy applications. This relation is well recognized: most textbooks and monographs on fuzzy sets and fuzzy techniques have a chapter on interval computation (Klir and Yuan have a chapter, Bojadziev's book is all devoted to this relation, etc.). INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: ADDITIONAL RELATIONS There are many other relations between fuzzy and intervals. For example, normally, a fuzzy set (e.g., the set of all small objects) is defined as a function m(x) which assigns, to every element x from a certain domain, the degree m(x) to which this element belongs to this fuzzily defined set. It is difficult to expect that we can come up with an exact value for this degree. It is more natural to assume that an expert provides us with an *interval* of possible values. Thus, we get the idea of "interval-valued" fuzzy sets, which have been successfully used by I. B. Turksen, L. Kohout, J. Mendel, and many other researchers. Handling interval-valued functions requires a lot of interval computations. INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: PROBLEMS Many researchers use interval techniques in fuzzy applications. However, often, they use outdated (1960s') interval techniques where more advanced techniques would lead to much more effective and efficient results. This disconnect is caused by two reasons: * On one hand, many researchers in the area of fuzzy methods are not very familiar with the latest advances in interval computations. * On the other hand, many interval researchers are not very familiar with problems and methods of fuzzy techniques. INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: UNIQUE OPPORTUNITY Right now, there is a great opportunity to narrow the gap between interval and fuzzy communities. In June 25-28, 2001, there will be a major event: a joint conference of the North American Fuzzy Information Processing Society (NAFIPS) and the International Fuzzy Systems Association (IFSA) in Vancouver (see CFP below). The organizers of this joint conference realized that this disconnect harms both communities and prevents them from even more successful applications. Therefore, they suggested that we organize a special mini-track on interval computations and fuzzy techniques. The intention is that this mini-track include: * technical and applied talks on successes and problems of interval methods in fuzzy techniques; * survey talks by *interval* researchers on the existing interval techniques; * technical talks of *interval* researchers on new algorithms which may be of use in fuzzy applications; * talks by *fuzzy* researchers on interval-related fuzzy problems which may benefit from using improved interval algorithms; * any related talks on techniques which generalize interval and/or fuzzy approaches. THIS IS REALLY URGENT To provide maximum publicity to this endeavor, the organizers of NAFIPS'01 want to publicize it during this year's IEEE Conference FUZZIEEE'2000 which will take place in early May. To be able to do that, they need to have the preliminary idea of this mini-track by May 1, 2000. This list does not have to be final, but it will be used to advertise the conference and its interval mini-track. Since I am very familiar with both communities, I volunteered to serve as a preliminary contact point for this mini-track. I have already talked with several renown researchers who have successfully combined interval and fuzzy techniques, and many expressed their interest in presenting their results at this mini-track. But to have an impact, to provide a breakthrough, we need as many researchers and papers as possible. If you are interested in presenting a talk at this mini-track, please send me (by email) your name and the preliminary title of your talk (abstract is also great, but if it is difficult to produce an abstract at short notice, abstracts are only due by December 15). Let us all together make a difference! Yours Vladik Vladik Kreinovich Department of Computer Science University of Texas at El Paso El Paso, TX 79968, USA email vladik@utep.edu