FUZZY INTEGERS AND METHODS OF CONSTRUCTING THEM TO REPRESENT UNCERTAIN OR IMPRECISE INTEGER INFORMATION

摘要

In this paper the concept of fuzzy integers which can be used to represent uncertain or imprecise integer quantity is proposed, the properties of fuzzy integers are investigated, and a representation theorem of fuzzy integers is obtained. Based on the representation theorem, the closeness of operation for fuzzy integers is discussed, it is shown that the usual addition still preserves the closeness of operation for fuzzy integers, but the usual multiplication and scalar multiplication do not preserve the closeness of the operation for fuzzy integers, and a new multiplication and a new scalar multiplication which preserve the closeness of operation for fuzzy integers are defined. Then for the sake of convenience and more rationality in application, a special kind of fuzzy integers which is called trapezoid-type fuzzy integer is introduced, and a method constructing trapezoid-type fuzzy integers to represent uncertain or imprecise integer quantities is proposed. At last, two practical examples are given to show the method of constructing fuzzy integers to represent uncertain or imprecise integer quantities.