Fuzzy absolute error distance measure based on a generalised difference operation

The main goal of this paper is to introduce a notion of fuzzy absolute error distance measure between two fuzzy numbers. For this purpose, a notion of generalised difference operation between two fuzzy numbers and absolute value of a fuzzy number was first introduced. The proposed methods were conducted on the basis of α-values of fuzzy numbers. Main properties of the proposed fuzzy distance measure was also verified in the space of fuzzy numbers. The proposed fuzzy distance measure evaluates the fuzzy distance between the two fuzzy numbers as a fuzzy number. Notably, the main advantage of such generalised difference operation is that it always exists. Therefore, it improves the shortcoming of a well-known generalised difference operation called Hakuhara difference. Some of the main properties of the proposed fuzzy absolute error distance measure including robustness were also studied in the space of fuzzy numbers. Several fuzzy distance measures, especially fuzzy absolute error distance, have been proposed so far. However, none of them save all reasonable properties required for an absolute error distance measure in fuzzy environment. Shortcomings relevant to other methods and advantages of the proposed method were also discussed.