Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10324156 | Fuzzy Sets and Systems | 2005 | 19 Pages |
Abstract
The usual concept of differentiability of fuzzy-number-valued functions, has the following shortcoming: if c is a fuzzy number and g:[a,b]âR is an usual real-valued function differentiable on x0â(a,b) with gâ²(x0)⩽0, then f(x)=câg(x) is not differentiable on x0. In this paper we introduce and study generalized concepts of differentiability (of any order nâN), which solves this shortcoming. Newton-Leibnitz-type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied. Also, some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form câg(x), are given.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Barnabás Bede, Sorin G. Gal,