Akbar H. Borzabadi, Mohammad Heidari, Delfim F. M. Torres
{"title":"Alternative views on fuzzy numbers and their application to fuzzy differential equations","authors":"Akbar H. Borzabadi, Mohammad Heidari, Delfim F. M. Torres","doi":"arxiv-2407.07906","DOIUrl":null,"url":null,"abstract":"We consider fuzzy valued functions from two parametric representations of\n$\\alpha$-level sets. New concepts are introduced and compared with available\nnotions. Following the two proposed approaches, we study fuzzy differential\nequations. Their relation with Zadeh's extension principle and the generalized\nHukuhara derivative is discussed. Moreover, we prove existence and uniqueness\ntheorems for fuzzy differential equations. Illustrative examples are given.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.07906","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.