On fuzzy differential equations in the quotient space of fuzzy numbers
| Autor: | Chongxia Lu, Dong Qiu, Wei Zhang |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
0209 industrial biotechnology Pure mathematics Fuzzy classification Mathematics::General Mathematics Logic 02 engineering and technology Quotient space (topology) Fuzzy subalgebra Defuzzification 020901 industrial engineering & automation Artificial Intelligence 0202 electrical engineering electronic engineering information engineering Fuzzy set operations Fuzzy number 020201 artificial intelligence & image processing Fuzzy associative matrix Equivalence class Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 295:72-98 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2015.03.010 |
| Popis: | Since addition possesses an inverse in the quotient space of fuzzy numbers based on Mares equivalence relation, in this paper, we introduce a metric on the quotient space of fuzzy numbers, and then deal with fuzzy mappings of a real variable whose values are equivalence classes of fuzzy numbers. We study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation. Finally, some examples are given to illustrate the main theorems. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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