Abstract
In daily life, we use information obtained to understand our surroundings, to learn new things, and to make plans for the future. Over the years, we have developed the ability to reason on the basis of evidence in order to achieve our goals. However, since we are restricted by our ability to perceive the world, we find ourselves always confronted by uncertainties about how good our inferences are. Uncertainties are one of the sources from which our errors stem since we do not know the exact information about our environment.
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Bibliography
D. Driankov, H. Hellendoorn, and M. Reinfrank, An Introduction to Fuzzy Control, 2nd Ed., New York: Springer-Verlag, 1996.
G. J. Klir, U. St. Clair, and B. Yuan, Fuzzy Set Theory: Foundations and Applications, Upper Saddle River, NJ: Prentice Hall, 1997.
H. Liang, H. Zhang, and D. Liu, “Roughness of fuzzy sets based on two new operators,” Proceedings of the IEEE International Conference on Fuzzy Systems, Budapest, Hungary, July 2004, pp 583–586.
T. Y. Lin and N. Cercone, Eds., Rough Sets and Data Ming: Analysis of Imprecise Data Norwell, MA: Kluwer Academic Publishers, 1996.
K. Passino and S. Yurkovich, Fuzzy Control, Menlo Park, CA: Addison-Wesley, 1998.
Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, pp. 341–356, 1982.
Z. Pawlak, Rough Sets-Theoretical Aspects of Reasoning about Data, Boston, MA, USA: Kluwer Academic Publishers, 1991.
Z. Pawlak, “Rough set theory and its applications to data analysis,” Cybernetics and Systems, vol. 29, no. 7, pp. 661–688, Oct.–Nov. 1998.
L. Polkowski and A. Skowron, Eds., Rough Sets in Knowledge Discovery: Applications, Case Studies and Software Systems, New York: Springer-Verlag, 1998.
R. Slowinski, Ed., Intelligent Decision Support: Handbook of Applications and Advances of the Rough Set Theory, Norwell, MA: Kluwer Academic Publishers, 1992.
L. Wang. A Course in Fuzzy Systems and Control, Upper Saddle River, NJ: Prentice Hall. 1997.
I. Yen and R. Langari, Fuzzy Logic: Intelligence, Control, and Information, Upper Saddle River, NJ: Prentice Hall, 1999.
L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Transaction on Systems. Man. and Cybernetics, vol. SMC-3, no. 1, pp. 28–44, 1973.
L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I, II, III,” Information Sciences, vol. 8, no. 3, pp. 199–249; vol. 8, no. 4, pp. 301–357; vol. 9, no. 1, pp. 43–80, 1975.
H. Zhang, H. Liang, and D. Liu, “Two new operators in rough set theory with applications to fuzzy sets,” Information Sciences, vol. 166, no. 1–4, pp. 147–165. Oct. 2004.
H. J. Zimmermann, Fuzzy Set Theory and Its Application, Netherlands: Kluwer-Nijhoff, 1985.
K. Zou and Y. Xu, Fuzzy Systems and Expert Systems, Sichuan, China: Southwest Jiaotong University Press, 1989.
Proceedings of the 4th International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery, Tokyo, Japan, Nov. 1996.
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(2006). Fuzzy Set Theory and Rough Set Theory. In: Fuzzy Modeling and Fuzzy Control. Control Engineering. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4539-7_1
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DOI: https://doi.org/10.1007/978-0-8176-4539-7_1
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