Two-dimensional discrete fuzzy numbers and applications

In this paper, the concept of two-dimensional discrete fuzzy numbers is presented based on the idea of representation theorem of one-dimensional discrete fuzzy numbers. Then a sufficient condition is proposed, which makes a fuzzy set on R2 become a two-dimensional discrete fuzzy number, and the representations of joint membership function and the two edge membership functions of two-dimensional discrete fuzzy number are given. Some special two-dimensional discrete fuzzy numbers are also defined. And then some weak orders in the two-dimensional discrete fuzzy number space are set up based on the mass centers and the degree of ambiguities of two-dimensional discrete fuzzy numbers, and their properties are also investigated. At last, some practical examples are included to demonstrate the effectiveness and potential of the theoretic results obtained.