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The Uncertainty Measure of Hierarchical Quotient Space Structure
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-02-06
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
In the application of fuzzy reasoning, researchers usually choose the membership function optionally in some degree.
Even though the membership functions may be different for the same concept, they can generally get the same (or approximate) results.
The robustness of the membership function optionally chosen has brought many researchers' attention.
At present, many researchers pay attention to the structural interpretation (definition) of a fuzzy concept, and find that a hierarchical quotient space structure may be a better tool than a fuzzy set for characterizing the essential of fuzzy concept in some degree.
In this paper, first the uncertainty of a hierarchical quotient space structure is defined, the information entropy sequence of a hierarchical quotient space structure is proposed, the concept of isomorphism between two hierarchical quotient space structures is defined, and the sufficient condition of isomorphism between two hierarchical quotient space structures is discovered and proved also.
Then, the relationships among information entropy sequence, hierarchical quotient space structure, fuzzy equivalence relation, and fuzzy similarity relation are analyzed.
Finally, a fast method for constructing a hierarchical quotient space structure is presented.
American Psychological Association (APA)
Zhang, Qinghua& Wang, Guoyin. 2011. The Uncertainty Measure of Hierarchical Quotient Space Structure. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-477583
Modern Language Association (MLA)
Zhang, Qinghua& Wang, Guoyin. The Uncertainty Measure of Hierarchical Quotient Space Structure. Mathematical Problems in Engineering No. 2011 (2011), pp.1-16.
https://search.emarefa.net/detail/BIM-477583
American Medical Association (AMA)
Zhang, Qinghua& Wang, Guoyin. The Uncertainty Measure of Hierarchical Quotient Space Structure. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-477583
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-477583