A top-down algorithm for generating the Hasse tree of a fuzzy preorder closure

IEEE Transactions on Fuzzy Systems

Volumn 12, Issue 6, 2004, Pages 838-848

  De Baets, Bernard ^a   De Meyer, Hans ^a   Naessens, Helga ^b  

^a GHENT UNIVERSITY   (Belgium)

^b UNIVERSITY COLLEGE GHENT   (Belgium)

Author keywords

Fuzzy preorder; Fuzzy relation; Hasse diagram; Hasse tree; Transitive closure

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; THEOREM PROVING; TREES (MATHEMATICS);

FUZZY PREORDER; FUZZY RELATION; HASSE DIAGRAM; HASSE TREE; TOP DOWN ALGORITHM; TRANSITIVE CLOSURE;

FUZZY SETS;

EID: 10944245745     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2004.836083     Document Type: Article

References (16)

1. W. Bandler and L. Kohout, "Fuzzy relational products as a tool for analysis and synthesis of the behavior of complex natural and -artificial systems," in Fuzzy Sets: Theory and Application to Policy Analysis and Information Systems, S. Wang and P. Chang, Eds. New York: Plenum Press, 1980, pp. 341-367.
2. W. Bandler and L. Kohout, "Special properties, closures, and interiors of crisp and fuzzy relations," Fuzzy Sets Syst., vol. 26, pp. 317-331, 1988.
3. B. De Baets, "Ordering alternatives in MCDM problems," in Fuzzy Logic and Intelligent Technologies in Nuclear Science, D. Ruan et al., Eds. Singapore: World Scientific, 1994, pp. 48-53.
4. B. De Baets, H. De Meyer, and H. Naessens, "On rational cardinality-based inclusion measures," Fuzzy Sets Syst., vol. 128, pp. 169-183, 2002.
5. B. De Baets and H. De Meyer, "On the existence and construction of T transitive closures," Inform. Sci., vol. 152, pp. 167-179, 2003.
6. H. De Meyer, H. Naessens, and B. De Baets, "Algorithms for computing the min-transitive closure and associated partition tree of a symmetric fuzzy relation," Eur. J. Oper. Res., vol. 155, pp. 226-238, 2004, to be published.
7. J. Fodor and M. Roubens, Fuzzy Preference Modeling and Muticriteria Decision Support. Dordrecht, The Netherlands: Kluwet, 1994.
8. R. Groenemans, E. Kerre, and E. Van Ranst, "Fuzzy relational calculus in land evaluation," GEODERMA, vol. 77, pp. 283-298, 1997.
9. E. Haven, "The fuzzy multicriteria analysis method: An application on NPV ranking," Int. J. Intell. Syst. Acc. Fin. Manage., vol. 7, pp. 243-252, 1998.
10. B. A. Juliano and W. Bandler, "Studies in fuziness," in Tracing Chains-of-Thought. Heidelberg, Germany: Physica-Verlag, 1996, vol. 7.
11. 2) algorithm for computing the min-transitive closure of a weighted graph," Inform. Proc. Lett., vol. 74, pp. 215-220, 2000.
12. H. Naessens, B. De Baets, and H. De Meyer, "Generating Hasse trees of fuzzy preorder closures: An algorithmic approach," in Proc. 1999 Joint EUSFLAT-ESTYLF Conf., Palma de Mallorca, Spain, 1999, pp. 387-390.
13. H. Naessens, H. De Meyer, and B. De Baets, "Algorithms for the computation of T-transitive closures," IEEE Trans. Fuzzy Syst. vol. 10, pp. 541-551, June 2002.
14. B. Van de Walle, B. De Baets, and E. Kerre, "Fuzzy multi-criteria analysis of cutting techniques in a nuclear reactor dismantling project," Fuzzy Sets Syst., vol. 74, pp. 115-116, 1995.
15. B. Van de Walle, B. De Baets, and E. Kerre, "Characterizable fuzzy preference structures," Ann. Oper. Res., vol. 80, pp. 105-136, 1998.
16. L. Zadeh, "Similarity relations and fuzzy orderings," Inform. Sci. vol. 3, pp. 177-200, 1971.