Abstract
The relationship of vague sets and fuzzy sets is analyzed and the problem of transforming vague sets into fuzzy sets is studied in this paper. It is found to be a many-to-one mapping relation to transform a vague set into a fuzzy set. A general model for transforming vague sets into fuzzy sets is proposed. The two transforming methods proposed by Fan Li in [1] are proved to be two special cases of this general transforming model.
This paper is partially supported by National Natural Science Foundation of P.R. China(No.60373111, No.60573068), New Century Excellent Talents in University, Natural Science Foundation of Chongqing(No.2005BA2003), and Science and Technology Research Program of Chongqing Education Commission(No. 040505).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Li, F., Lu, Z., Cai, L.J.: The entropy of vague sets based on fuzzy sets. Journal of Huazhong University of Science and Technology (Nature Science Edition) 1, 1–3 (2003)
Zadeh, L.A.: Fuzzy sets. Information and Control 3, 338–353 (1965)
Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Transactions on Systems, Man and Cybemetics 2, 610–614 (1993)
Xu, J.C., An, Q.S., Wang, G.Y., Shen, J.Y.: Disposal of information with uncertain borderline-fuzzy sets and vague sets. Computer Engineering and Applications 16, 24–26 (2002)
Cai, L.J., Lv, Z.H., Li, F.: A three-dimension expression of vague set and similarity measure. Computer Science 5, 76–77 (2003)
Li, F., Lu, A., Yu, Z.: A construction method with entropy of vague sets based on fuzzy sets. Journal of Huazhong University of Science and Technology (Nature Science Edition) 9, 1–2 (2001)
Li, F., Xu, Z.Y.: Measure of similarity between vague sets. Journal of Software 6, 922–926 (2001)
Ma, Z.F., Xing, H.C.: Strategies of ambiguous rule acquisition from vague decision table. Chinese Journal of Computers 4, 382–389 (2001)
Chen, S.M.: Measures of similarity between vague sets. Fuzzy Sets and Systems 2, 217–223 (1995)
Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 3, 403–405 (1996)
Chen, S.M.: Similarity Measures Between Vague Sets and Between Elements. IEEE Transactions on Systems, Man, and Cybernetics, PartB: Cybernetics 1, 153–158 (1997)
Hong, D.H., Chul, K.: A note on similaity measures between vague sets and between elements. Information sciences 1-4, 83–96 (1999)
Hong, D.H., Choi, C.H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 1, 103–113 (2000)
Lin, Z.G., Liu, Y.P., Xu, L.Z., Shen, Z.Y.: A method for transforming vague sets into fuzzy sets in fuzzy information processing. Computer Engineering and Applications 9, 24–25 (2004)
Li, F., Lu, A., Cai, L.J.: Fuzzy entropy of vague sets and its construction method. Computer Applications and Software 2, 10–12 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, Y., Wang, G., Feng, L. (2006). A General Model for Transforming Vague Sets into Fuzzy Sets. In: Wang, GY., Peters, J.F., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2006. Lecture Notes in Computer Science(), vol 4062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795131_49
Download citation
DOI: https://doi.org/10.1007/11795131_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36297-5
Online ISBN: 978-3-540-36299-9
eBook Packages: Computer ScienceComputer Science (R0)