Hybrid monotonic inclusion measure and its use in measuring similarity and distance between fuzzy sets

Fuzzy Sets and Systems

Volumn 160, Issue 1, 2009, Pages 107-118

  Zhang, Hong Ying ^a   Zhang, Wen Xiu ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Distance; Fuzzy sets; Inclusion measure; Similarity measure

Indexed keywords

LEARNING SYSTEMS; SET THEORY;

DISTANCE; DISTRIBUTIVITY; FUZZY SET THEORIES; FUZZY-SET; INCLUSION RELATIONS; MEASURING; SIMILARITY MEASURE; SIMILARITY MEASURES;

FUZZY SETS;

EID: 54549115012     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2008.06.002     Document Type: Article

References (38)

1. Bandler W., and Kohout L. Fuzzy power sets and fuzzy implication operators. Fuzzy Sets and Systems 4 (1980) 13-30
2. Bělohlávek R. Fuzzy Relational Systems: Foundations and Principles (2002), Kluwer Academic, Plenum Publishers, New York
3. Bodjanova S. Approximation of fuzzy concepts in decision making. Fuzzy Sets and Systems 85 (1997) 23-29
4. Cornelis C., Donck C.V., and Kerre E.E. Sinha-Dougherty approach to the fuzzification of set inclusion revisited. Fuzzy Sets and Systems 134 (2003) 283-295
5. De Baets B., De Meyer H., and Naessens H. A class of rational cardinality-based similarity measures. J. Comput. Appl. Math. 132 (2001) 51-69
6. De Baets B., De Meyer H., and Naessens H. On rational cardinality-based inclusion measures. Fuzzy Sets and Systems 128 (2002) 169-183
7. Fan J.L., and Xie W.X. Some notes on similarity measure and proximity measure. Fuzzy Sets and Systems 101 (1999) 403-412
8. Fan J.L., Xie W.X., and Pei J.H. Subsethood measure: new definitions. Fuzzy Sets and Systems 106 (1999) 201-209
9. Fan S.Q., Zhang W.X., and Xu W. Fuzzy inference based on fuzzy concept lattice. Fuzzy Sets and Systems 157 (2006) 3177-3187
10. N. Frago, Morfología mátematica Borrosa Basada en operadores generalizados de Łukasiewicz: Procesamiento de imágenes, Ph.D. Thesis, Universidad Pública de Navarra, 1996.
11. Kaburlasos V.G., and Petridis V. Fuzzy lattice neurocomputing (FLN): a novel connectionist scheme for versatile learning and decision making by clustering. Internat. J. Comput. Appl. 4 (1997) 31-43
12. Kehagias A., and Konstantinidou M. L-fuzzy valued inclusion measure, L-fuzzy similarity and L-fuzzy distance. Fuzzy Sets and Systems 136 (2003) 313-332
13. Kerre E.E., Cao C.F., and Ruan D. Fuzzy Set Theory and Approximate Reasoning (2004), Wuhan University Press
14. Klir G.J., and Yuan B. Fuzzy Logic: Theory and Applications (1995), Prentice-Hall, Englewood Cliffs, NJ
15. Kosko B. Fuzzy entropy and conditioning. Inform. Sci. 40 (1986) 165-174
16. Kosko B. Neural Networks and Fuzzy Systems (1992), Prentice-Hall, Englewood Cliffs, NJ
17. Kundu S. A representation theorem for min-transitive fuzzy relations. Fuzzy Sets and Systems 109 (2000) 453-457
18. Liu X.C. Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems 52 (1992) 305-318
19. Ma Z., Zhang W., and Ma W. Assessment of data redundancy in fuzzy relational databases based on semantic inclusion degree. Inform. Process. Lett. 72 (1999) 25-29
20. Pappis C.P. Value approximation of fuzzy systems variables. Fuzzy Sets and Systems 39 (1991) 111-115
21. Pappis C.P., and Karacapilidis N.I. Application of a similarity measure of fuzzy sets to fuzzy relational equations. Fuzzy Sets and Systems 75 (1992) 135-142
22. Pappis C.P., and Karacapilidis N.I. A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems 56 (1993) 171-174
23. Petridis V., and Kaburlasos V.G. Fuzzy lattice neural network (FLNN): a hybrid model for learning. IEEE Trans. Neural Networks 9 (1998) 877-890
24. Qiu G.F., Li H.Z., Xu L.D., and Zhang W.X. A knowledge processing method for intelligent systems based on inclusion degree. Expert systems 20 (2003) 187-195
25. Radzikowska A.M., and Kerre E.E. A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126 (2002) 137-155
26. Sinha D., and Dougherty E.R. Fuzzification of set inclusion: theory and applications. Fuzzy Sets and Systems 55 (1993) 15-42
27. Smets P., and Magrez P. Implication in fuzzy logic. Internat. J. Approx. Reasoning 1 (1987) 327-347
28. Wang W.J. New similarity measures on fuzzy sets and elements. Fuzzy Sets and Systems 85 (1997) 305-309
29. Wang X.Z., De Baets B., and Kerre E.E. A comparative study of similarity measures. Fuzzy Sets and Systems 73 (1995) 259-268
30. Willmott R. Two fuzzier implication operators in the theory of fuzzy power sets. Fuzzy Sets and Systems 4 (1980) 31-36
31. Willmott R. On the transitivity of containment and equivalence in fuzzy power set theory. J. Math. Anal. Appl. 120 (1986) 384-396
32. Xu Z.B., Liang J.Y., Chen D.G., and Chin K. Inclusion degree: a perspective on measures for rough set data analysis. Inform. Sci. 141 (2002) 227-236
33. Young V.R. Fuzzy subsethood. Fuzzy Sets and Systems 77 (1996) 371-384
34. Zadeh L.A. Fuzzy sets. Inform. Control 8 (1965) 338-353
35. Zhang W.X., and Leung Y. The Uncertainty Reasoning Principles (1996), Xi'an Jiaotong University Press, Xi'an
36. Zhang W.X., and Leung Y. Theory of including degrees and its applications to uncertainty inferences. Soft Computing in Intelligent Systems and Information Processing (1996), IEEE, New York 496-501
37. Zhang W.X., Leung Y., and Wu W.Z. Information Systems and Knowledge Discovery (2003), Science Press, Beijing
38. Zhang W.X., and Qiu G.F. Uncertain Decision Making Based on Rough Sets (2005), Tsinghua University Press, Beijing