Abstract
In this paper, the definition of generalized discrete fuzzy numbers is introduced, and a representation theorem of such fuzzy numbers is obtained. Based on the representation theorem, it is shown that the usual addition and multiplication which are defined by Zadeh’s extension principle do not preserve the closeness of the operation, and a new addition operation and a new multiplication operation are defined, which not only preserve the closeness of the operation, but also are easy to calculate. Then some weak orders on the generalized discrete fuzzy number space are defined, and their properties are investigated. At last, a practical example is given to show the application of the algorithmic version to rank uncertain or imprecise discrete quantity.
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