Fuzzy inequality relation system identification via sign matrix method

This paper intends to propose a new method of solving fuzzy relation inequality system identification which is expressed as B_⩽RoA⩽B¯. A is the input vector of the system; B¯, B_ is the upper bound and lower bound of the output vector of the system. R is an unknown fuzzy number matrix which represents the considered system. This is an extension and reverse problem of solving fuzzy relation equation RoA=B, and it has a very promising application scope in fuzzy system theory. In the proposed method, a so called sign matrix will be introduced and plays the main role. The element of the sign matrix is one of three kinds of signs `<´, `=´ and `>´. Some related properties about this topic will be discussed. We will also extend the sign matrix method to the problem of fuzzy relation system with interval valued input and output