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.
discrete fuzzy numbers fuzzy numbers weak orders ranking