A new approach for ranking nonnormal pp-norm trapezoidal fuzzy numbers

Ranking of fuzzy numbers play an important role in decision-making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that the results proposed by Chen and Tang [C.C. Chen, H.C. Tang, Ranking of nonnormal pp-norm trapezoidal fuzzy numbers with integral value, Computers and Mathematics with Applications 56 (2008) 2340–2346] are applicable only for the nonnormal pp-norm trapezoidal fuzzy numbers with equal heights and a new approach is proposed for the ranking of nonnormal pp-norm trapezoidal fuzzy numbers with different heights. The results proposed by Chen and Tang are modified and to illustrate the proposed approach the counter examples are solved using the proposed approach. It is also shown that the proposed approach and the results, obtained by using the proposed approach, are valid.