## Hung T. Nguyen Selected as a Distinguished Lukacs Professor

Professor Hung T. Nguyen from New Mexico State University has been selected as a Distinguished Lukacs Professor in Statistics at the Bowling Green State University for Spring 2002.

This position is one of the world's most prestigious in mathematical statistics. Previous appointees include renown statisticians such as Gabor Szekely (1991), Anatoly Skorokhod (1994), and C.R. Rao (1998).

This position was established in 1989 in the memory of Eugene Lukacz, a world renown statistician. Lukacz's research covered many areas of statistics, including his pioneering analysis of robustness (stability) of statistical characterization results. Many theoretical results of mathematical statistics are based on certain assumptions about the corresponding distributions. In practice, these assumptions can only be checked with a certain accuracy; so, the natural question is: if we know that the assumption holds with a certain accuracy, is it true that the conclusion holds with some accuracy? The answer to this questions requires that we consider classes of probability distributions, specifically, classes of all distributions which are consistent with the given measurement results and with the existing expert knowledge.

Professor Nguyen was selected for his numerous research accomplishments, including his 1970s results that fuzzy sets and their operations can be re-interpreted in more traditional statistical terms as appropriate classes of probability distributions, and his more recent interval-related research in which an interval is also interpreted as a class of all distributions located on it. Nguyen's results helped to make fuzzy and interval methods mainstream and acceptable to the statistical community.

### References:

The pioneer paper is:
H.T. Nguyen, Some mathematical tools for linguistic probabilities, Fuzzy Sets and Systems, vol. 2 (1979), pp. 53-65.
The main idea is that the membership function m(x) of a fuzzy set (i.e., a function m: X --> [0,1]) is interpreted as the class of random sets, i.e., the class of all probability distributions P on the set 2^X of all subsets of X for which, for every x in X, P({R: x in R})=m(x).

In particular, an interval can be interpreted as a particular case of a fuzzy set; in this case, we get a distribution which is concentrated with probability 1 on this particular interval.

This idea was further developed and exposed in several papers and books, in particular,

Hung T. Nguyen and I. R. Goodman, Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference, Kluwer, 1994.

B. Bouchon-Meunier, V. Kreinovich, A. Lokshin, and H.T. Nguyen, On the formulation of optimization under elastic constraints (with control in mind), Fuzzy Sets and Systems, vol. 81 (1996), pp. 5-29.

In this paper, the above idea is expanded to explaining fuzzy logic operations and fuzzy optimization.

John Goutsias, Ronald P. S. Mahler, and Hung T. Nguyen (eds.), Random Sets: Theory and Applications, Springer-Verlag, N.Y., 1997.

Hung T. Nguyen and Berlin Wu, An Introduction to Fuzzy Logic for Statistics, Wu Nan Book Company, Taipei, 2000.

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