Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-08-06
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept.
As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region).
In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished.
In this paper, firstly, a fuzziness-based uncertainty measure is proposed.
Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed.
Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty.
Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes.
These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence.
American Psychological Association (APA)
Yang, Jie& Xu, Taihua& Zhao, Fan. 2018. Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1207332
Modern Language Association (MLA)
Yang, Jie…[et al.]. Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance. Mathematical Problems in Engineering No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1207332
American Medical Association (AMA)
Yang, Jie& Xu, Taihua& Zhao, Fan. Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1207332
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1207332