The explicit solution of fuzzy singular differential equations using fuzzy Drazin inverse matrix

摘要

This paper aims to provide a fuzzy solution for fuzzy singular differential equations (FSDEs) in which the coefficient matrices and/or initial conditions are considered as fuzzy matrices and/or numbers. In addition, the fuzzy derivative is in the sense of the granular derivative. To achieve the aim, some new concepts such as the rank and index of fuzzy matrices, and granular inverse of a nonsingular fuzzy matrix are presented. Moreover, a fuzzy matrix called fuzzy Drazin inverse matrix is defined which has a pivotal role of a fuzzy inverse matrix of a singular fuzzy matrix. Furthermore, two approaches for finding the fuzzy Drazin inverse matrix are given. In order to present the solution of FSDEs, a definition of nth order granular derivative is presented. This paper closes with some examples showing the approach is capable of finding the solution of FSDEs.