Fuzzy sets and fuzzy differential equations (Q2754440)

In spite of all advancement in the theory of fuzzy sets, there are a few results on fuzzy differential equations. The paper presents some results in the stability version for fuzzy differential equation. The paper consists of 6 sections. Section 1 is an introduction. In section 2 the authors give basic concepts of fuzzy analysis of fuzzy (convex, concave) mappings. In sections 3 and 4, by using fuzzy convex sets and comparison principles, existence and uniqueness theorems are given. The continuous dependence of solutions to fuzzy differential equations on initial values are proved. In sections 5 and 6, the potentially important stability criteria on fuzzy differential equations are discussed by generalizing the concept of Lyapunov functions. Also the contraction mapping principle is generalized to obtain fixed-points of fuzzy mappings.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00018].