Fuzzy $n$-Ellipsoid Numbers and Representations of Uncertain Multichannel Digital Information

摘要

In this paper, we present the definition of fuzzy $n$ -ellipsoid numbers that are a special kind $n$-dimensional fuzzy numbers which are not only more objective and more rational in expressing uncertain multichannel digital information than are fuzzy $n$-cell numbers but keep the convenience being used in applications and researches of the theory as well. We also obtain two representation results. Then, for the sake of the application of fuzzy $n$-ellipsoid numbers, we define some special kinds of fuzzy $n$-ellipsoid numbers, investigate their properties, set up a specific iterative algorithm of their membership function value, and prove the convergence of the iterative algorithm. And then, we establish an algorithmic version of constructing fuzzy $n$-ellipsoid numbers to express an object that is characterized by a group of uncertain multichannel digital information, as well as give practical examples to show the application and rationality of the proposed techniques.