Ranking of generalized fuzzy numbers based on accuracy of comparison

Ranking generalized fuzzy numbers plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two generalized fuzzy numbers, it is natural to compare the sets of values in support of two generalised fuzzy numbers. Accordingly, the comparison of a real number and a generalised fuzzy number as well as two generalised fuzzy numbers have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised fuzzy number, as well as two generalised fuzzy numbers, is not possible. So in this study, a method for comparing a real number and a generalised fuzzy number with a degree of accuracy (between a zero and one) is defined and then the method is generalized to compare two generalised fuzzy numbers. In general, an index to rank a real number and generalised fuzzy number is constructed. Eventually, this index is extended to rank two generalised fuzzy numbers based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised fuzzy numbers with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples.

Keywords:

Fuzzy set , generalized , Ranking fuzzy numbers