Abstract
In this chapter we explore fuzziness as tool to capture uncertainty. Let S be a set and let A and B be subsets of S. We use the notation A ∪ B, A ∩ B to denote the union of A and B and intersection of A and B, respectively. Let B\A denote the relative complement of A in B. The (relative) complement of A in S,S\A, is sometimes denoted by A C when S is understood.
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References
Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications, Mathematics in Science and Engineering, Vol. 144, Academic Press, Inc., Orlando, Florida, 1980.
Kandel, A., Fuzzy Mathematical Techniques with Applications, Addison-Wesley Pub. Co. 1986.
Kaufmann, A., Introduction to the Theory of Fuzzy Sets, Vol. 1, Academic Press, Inc., Orlando, Florida, 1973.
Klir, G.J., U. St. Clair, U.H., and Yuan, B., Fuzzy Set Theory, Foundations and Applications, Prentice Hall, Upper Saddle River, N.J., 1997.
Klir, G.J. and Folger, T.A., Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, N.J., 1988.
Klir, G.J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, N.J., 1995.
Rosenfeld, A., Fuzzy graphs. In: L. A. Zadeh, K. S. Fu and M. Shimura, Eds., Fuzzy Sets and Their Applications, Academic Press, New York, 77–95, 1975.
Tamura, S., Higuchi, S., and Tanaka, K., Pattern Classification Based on Fuzzy Relations, IEEE Trans. SMC-1, 61–66, 1971.
Yeh, R. T. and Bang, S.Y., Fuzzy graphs, fuzzy relations, and their applications to cluster analysis. In: L. A. Zadeh, K. S. Fu and M. Shimura, Eds., Fuzzy Sets and Their Applications,Academic Press, New York, 125–149, 1975.
Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1: 3–28, 1978.
Zadeh, L.A., Similarity relations and fuzzy orderings, Information Sci., 3: 177–200, 1971.
Zimmermann, H.J., Fuzzy Set Theory and Its Applications, Second Edition, Kluwer Academic Publishers, Boston, Dordrecht/London, 1991.
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© 2001 Springer-Verlag Berlin Heidelberg
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Mordeson, J.N., Nair, P.S. (2001). Fuzzy Subsets. In: Fuzzy Mathematics. Studies in Fuzziness and Soft Computing, vol 20. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1808-6_1
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DOI: https://doi.org/10.1007/978-3-7908-1808-6_1
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2494-0
Online ISBN: 978-3-7908-1808-6
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