| Title:
|
Fuzzy-valued integrals based on a constructive methodology (English) |
| Author:
|
Wu, Hsien-Chung |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
1-23 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral of fuzzy-valued function with respect to fuzzy-valued measure. Finally, we provide a Dominated Convergence Theorem for fuzzy-valued integrals. (English) |
| Keyword:
|
dominated convergence theorem |
| Keyword:
|
fuzzy number |
| Keyword:
|
fuzzy-valued function |
| Keyword:
|
fuzzy-valued integral |
| Keyword:
|
resolution identity |
| MSC:
|
03E72 |
| MSC:
|
28E10 |
| idZBL:
|
Zbl 1164.28308 |
| idMR:
|
MR2293526 |
| DOI:
|
10.1007/s10492-007-0001-x |
| . |
| Date available:
|
2009-09-22T18:28:12Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134661 |
| . |
| Reference:
|
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