Alternative views on fuzzy numbers and their application to fuzzy differential equations

Document Type : Research Article

Authors

1 Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran

2 Young Researchers and Elite Club, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

3 Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Abstract

 We consider fuzzy valued functions from two parametric representations of $\alpha$-level sets. New concepts are introduced and compared with available notions. Following the two proposed approaches, we study fuzzy differential equations. Their relation with Zadeh's extension principle and the generalized Hukuhara derivative is discussed. Moreover,
we prove existence and uniqueness theorems for fuzzy differential equations. Illustrative examples are given.

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Journal of Mathematical Modeling
Volume 12, Issue 4
December 2024
Pages 623-654

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