Representation, ranking, distance, and similarity of fuzzy numbers with step form membership function using k-preference integration method

The modified k-preference integration method is applied to treat the representation, ranking; distance and similarity of fuzzy numbers with step form membership function. First, the representation value is computed by using the modified k-preference integration method. Then two or more fuzzy numbers with step form membership function are ranked by comparing their representation values. The distance between two fuzzy numbers with step form membership function is the absolute value of the difference between their representation values, while the similarity between them can be derived from their distance. Finally, some properties regarding the representation, ranking, distance, and similarity have been proved