Towards an (Even More) Natural Probabilistic Interpretation of Fuzzy Transforms (and of Fuzzy Modeling)
Joint Authors
Perfilieva, Irina G.
Kreinovich, Vladik
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-08-02
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Information Technology and Computer Science
Abstract EN
In many practical applications, it turns out to be useful to use the notion of fuzzy transform: once we have functions A1(x)≥0,...,An≥0, with ∑i=1nAi(x)=1, we can then represent each function f(x) by the coefficients Fi=(∫f(x)⋅Ai(x)dx)/(∫Ai(x)dx).
Once we know the coefficients Fi, we can (approximately) reconstruct the original function f(x) as ∑i=1nFi⋅Ai(x).
The original motivation for this transformation came from fuzzy modeling, but the transformation itself is a purely mathematical transformation.
Thus, the empirical successes of this transformation suggest that this transformation can be also interpreted in more traditional (nonfuzzy) mathematics as well.
Such an interpretation is presented in this paper.
Specifically, we show that the 2002 probabilistic interpretation of fuzzy modeling by Sánchez et al.
can be modified into a natural probabilistic explanation of fuzzy transform formulas.
American Psychological Association (APA)
Perfilieva, Irina G.& Kreinovich, Vladik. 2011. Towards an (Even More) Natural Probabilistic Interpretation of Fuzzy Transforms (and of Fuzzy Modeling). Advances in Fuzzy Systems،Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-493150
Modern Language Association (MLA)
Perfilieva, Irina G.& Kreinovich, Vladik. Towards an (Even More) Natural Probabilistic Interpretation of Fuzzy Transforms (and of Fuzzy Modeling). Advances in Fuzzy Systems No. 2011 (2011), pp.1-9.
https://search.emarefa.net/detail/BIM-493150
American Medical Association (AMA)
Perfilieva, Irina G.& Kreinovich, Vladik. Towards an (Even More) Natural Probabilistic Interpretation of Fuzzy Transforms (and of Fuzzy Modeling). Advances in Fuzzy Systems. 2011. Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-493150
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-493150