# Introduction to Fuzzy Logic

Chapter

In the early 1990s, scientists at the National Center for Atmospheric Research were asked to help the Federal Aviation Administration objectively determine which flight service stations throughout the United States handled the most hazardous weather conditions, and hence should be spared from congressional budget cuts. They had access to 15 years of meteorological data from each location, including winds, temperature, fog, rain, and snow at 1-min intervals, as well as information about the air traffic density and a number of other factors. However, the level of aviation hazard was not indicated by any single statistic, but by the nature, frequency and duration of the conditions and their combinations. How could the stations be ranked in a reasonable, objective way?

The scientists began by surveying a group of subject domain experts — pilots, meteorologists, and airline dispatchers — quizzing them on what factors, or combinations of factors, they considered most dangerous. Using the results of these surveys along with the repository of historical data, they then computed a hazard score for each flight service station, and ranked them. When the final report was presented to the group of experts, they opened it and began to laugh — everyone agreed that the stations with the most hazardous weather were at the top of the list. Unwittingly, the NCAR scientists had created a fuzzy logic algorithm, efficiently encoding the experts' knowledge in a set of rules that reproduced their approach to assessing the level of hazard presented by each unique set of weather conditions.

## Keywords

Membership Function Fuzzy Logic Fuzzy Number Fuzzy Rule Fuzzy Inference System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

1. Albo, D. (1994). Microburst detection using fuzzy logic. Termi-nal area surveillance system program project report (49 pp.). Washington, DC: Federal Aviation Administration. [Available from the author at NCAR, P. O. Box 3000, Boulder, CO 80307.]Google Scholar
2. Albo, D. (1996). Enhancements to the microburst automatic detection algorithm. Terminal area surveillance system program project report (47 pp.). Washington, DC: Federal Aviation Administration. [Available from the author at NCAR, P. O. Box 3000, Boulder, CO 80307.]Google Scholar
3. Chi, Z., Hong, Y., & Tuan, P. (1996). Fuzzy algorithms with applications to image processing and pattern recognition (225 pp.). River Edge, NJ: World ScientificGoogle Scholar
4. Delanoy, R. L., & Troxel, S. W. (1993). Machine intelligence gust front detection. Lincoln Laboratory Journal, 6, 187–211Google Scholar
5. Klir, G. J., & Folger, T. A. (1988). Fuzzy sets, uncertainty and information (355 pp.). Englewood Cliffs, NJ: Prentice HallGoogle Scholar
6. Klir, G. J., & Yuan, B. (Eds.). (1996). Fuzzy sets, fuzzy logic and fuzzy systems: Selected papers by Lotfi A. Zadeh (826 pp.). River Edge, NJ: World ScientificGoogle Scholar
7. Mamdami, E. H. (1974). Applications of fuzzy logic algorithms for control of a simple dynamic plant. Proceedings of IEEE, 121, 1585–1588Google Scholar
8. McNiell, D., & Freiberger, P. (1993). Fuzzy logic (319 pp.). New York: Simon & SchusterGoogle Scholar
9. Merritt, M. W. (1991). Microburst divergence detection for Terminal Doppler Weather Radar (TDWR). MIT Lincoln Laboratory project report ATC-181 (174 pp). Lexington, MA: MIT Lincoln LaboratoryGoogle Scholar
10. Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Man and Cybernetics, 15, 116–132Google Scholar
11. Tanaka, K. (1996). An introduction to fuzzy logic for practical applications (T. Tiimura, Trans., 138 pp.). New York: SpringerGoogle Scholar
12. Vivekanandan, J., Zrnic, D. S., Ellis, S. M., Oye, R., Ryzhkov, A. V., & Straka, J. (1999). Cloud microphysics retrieval using S-band dual polarization radar measurements. Bulletin of American Meteorological Society, 80, 381–388
13. Williams, J. K., & Vivekanandan, J. (2007). Sources of error in dual-wavelength radar remote sensing of cloud liquid water content. Journal of Atmospheric and Oceanic Technology, 24, 1317–1336
14. Yager, R. R., Ovchinnikov, S., Tong, R. M., & Nguyen, H. T. (Eds.) (1987). Fuzzy sets and applications: Selected papers by L. A. Zadeh (684 pp.). New York: WileyGoogle Scholar
15. Zadeh, L. H. (1965). Fuzzy sets. Information and Control, 8, 338–353
16. Zimmerman, H. J. (1996). Fuzzy set theory and its applications (435 pp.). Boston: KluwerGoogle Scholar

## Authors and Affiliations

1. 1.Research Applications LaboratoryNational Center for Atmospheric ResearchBoulderUSA