What are the definitions, theorems one need to know on the general theory of fuzzy differential equations?
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In the general theory of fuzzy differential equations, there are several important definitions and theorems to consider. One key concept is the fuzzy derivative, which is obtained by fuzzification of the classical derivative operator for standard functions . This approach is different from the traditional Hukuhara derivative defined for set-valued functions. Another important concept is the fuzzy integral, which is defined using the extension principle of Zadeh on the corresponding classical operator . Additionally, there are several theorems that have been established in the field. These include the fuzzy intermediate value theorem, fuzzy mean value theorem for integrals, and mean value theorem for the fuzzy derivative . Other theorems address the existence of solutions for fuzzy differential equations and provide comparison results for the solutions . These definitions and theorems form the foundation of the general theory of fuzzy differential equations.
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31 Aug 2012 9 Citations | The paper does not provide specific definitions or theorems on the general theory of fuzzy differential equations. |
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11 Apr 2018 | The provided paper does not discuss the general theory of fuzzy differential equations. |
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