The discrete fuzzy numbers on a fixed set with finite support set

It is known that to deep systematically study the theory in relation to general discrete fuzzy numbers always will encounter some difficulties since the metric and the difference of two general discrete fuzzy numbers cannot reasonably be defined. In this paper, we define a special sort discrete fuzzy numbers-discrete fuzzy number on a fixed set with finite support set, on which we can study the problems of metric and difference (we will study the problems in relation to metric and difference in afterwards papers). And then we obtain a representation theorem of such discrete fuzzy numbers, study the operations of scalar product, addition and multiplication, and obtain some results.