Interval sessions at NAFIPS/IFIS/NASA'94

At the suggestion of Reza Langari and John Yen, we announced a special session devoted to applications of interval methods to expert systems and fuzzy control. The number of contributors exceed our expectations, so at the conference, we had three sessions (out of 24) devoted to filzzy intervals. These sections were chaired Several interval-related papers were presented at other sessions. Totally, interval papers were authored by 27 authors from 8 countries: These sessions were atteilded by leading researchers in the field, and we hope" that the~' further promoted the understanding between the interval and the expert system communities. A well-organized social program, that included a boat tour of the San Antonio Riverwalk, a walking tour of the Alamo (the "Shrine of Texas Freedom"), and a bus tour of the Old City, definitely helped researchers to make informal contacts. Why fuzzy intervals? One of the main applications of expert knowledge is intdligenl control. In many cases, we want to design an automated controller, but do not know the exact behavior of the controlled plant, and we cannot therefore use traditional control techniqnes, In such cases, we often have the expertise of human controllers who know how to control the plant (e.g., how to drive a car, how to ride a plane, etc). These experts cannot formulate how exactly they control in exact terms. Instead, they can formulate their expertise in terms of "if-then" rules of the type: "if the obstacle is nearby, and you are driving with a moderate speed, hit the breaks immediatelyL There exists a methodology that transforms experts' rules, formulated in terms of words of a natural language, into a precise control strategy. This methodology is called fuzzy conlrol (see, e.g., [9]). Fuzzy control technique starts with determining the values of the membership fimctions #~(:r) that correspond to different words used in the rules. Namely, the value /~a(:r) represents the expert's degree of belief that a value :r satisfies the property A. Then~ it computes the degrees of belief in composite statements, and in particular, computes, for each