The generalized LR-fuzzy numbers and its application in fully fuzzy linear systems
The fully fuzzy linear systems (shown as FFLS) plays an essential role in fuzzy modelling, which can formulate uncertainty in actual environment. Recently, Dehghan et al. [M, Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Applied Mathematics. and Computation 179 (2006) 328-343.] gave the positive fuzzy solution of nonnegative FFLS (A) over tilde(x) over tilde = (b) over tilde, where (A) over tilde and (b) over tilde are a fuzzy matrix and a fuzzy vector, respectively. When the positive fuzzy solution does not exist or the fuzzy solution has negative spreads, it has not been investigated any further in the existing literatures. In this paper, we extend the definition of LR-fuzzy numbers, which we call generalized LR-fuzzy numbers, and develop its fuzzy arithmetic operations. Moreover, we study the fuzzy approximate solutions of FFLS based on GLR-fuzzy numbers, and analyze its solvability. An numerical example for calculating the fuzzy solution to FFLS is given.
lr-fuzzy numbers fuzzy matrix fully fuzzy linear systems (ffls)