# Article

Full entry | PDF   (1.9 MB)
Keywords:
fuzzy set; polynomial-time algorithms
Summary:
Let ${\cal A},\,{\cal B}$ be the strings of fuzzy sets over ${\chi }$, where ${\chi }$ is a finite universe of discourse. We present the algorithms for operations on fuzzy sets and the polynomial time algorithms to find the string ${\cal C}$ over ${\chi }$ which is a closest common subsequence of fuzzy sets of ${\cal A}$ and ${\cal B}$ using different operations to measure a similarity of fuzzy sets.
References:
[1] Andrejková G.: The longest restricted common subsequence problem. In: Proc. Prague Stringology Club Workshop’98, Prague 1998, pp. 14–25
[2] Andrejková G.: The set closest common subsequence problem. In: Proceedings of 4th International Conference on Applied Informatics’99, Eger–Noszvaj 1999, p. 8
[3] Gottwald S.: Fuzzy Sets and Fuzzy Logic. Vieweg, Wiesbaden 1993, p. 216 MR 1218623 | Zbl 0782.94025
[4] Hájek P.: Mathematics of Fuzzy Logic. Kluwer, Dordrecht 1998
[5] Hirschberg D. S.: Algorithms for longest common subsequence problem. J. Assoc. Comput. Mach. 24 (1977), 664–675 DOI 10.1145/322033.322044 | MR 0461985
[6] Hirschberg D. S., Larmore L. L.: The set LCS problem. Algorithmica 2 (1987), 91–95 DOI 10.1007/BF01840351 | MR 1554313 | Zbl 0642.68065
[7] Hirschberg D. S., Larmore L. L.: The set-set LCS problem. Algorithmica 4 (1989), 503–510 DOI 10.1007/BF01553904 | MR 1019389 | Zbl 0684.68080
[8] Kaufmann A.: Introduction to Theory of Fuzzy Subsets. Vol. 1: Fundamental Theoretical Elements. Academic Press, New York 1975 MR 0485402
[9] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[10] Mohanty S. P.: Shortest string containing all permutations. Discrete Math. 31 (1980), 91–95 DOI 10.1016/0012-365X(80)90177-6 | MR 0578066 | Zbl 0444.05014
[11] Nakatsu N., Kombayashi, Y., Yajima S.: A longest common subsequence algorithm suitable for similar text strings. Acta Inform. 18 (1982), 171–179 MR 0687701
[12] Zadeh L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978), 3–28 DOI 10.1016/0165-0114(78)90029-5 | MR 0480045

Partner of