This paper proposes a new method on ranking fuzzy numbers through the process of defuzzification by using maximizing and minimizing set on the triangular fuzzy numbers formed from generalized trapezoidal fuzzy numbers. In this method, a total utility value of each fuzzy number is defined by considering two left and two right utility values along with decision maker’s optimism which serves as a criterion for ranking fuzzy numbers and overcomes the limitations of Chen's (1985) [Chen, S. H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems, 17(2), 113-129] ranking method.

Very recently, Qiupeng and Zuxing (2017) [Qiupeng, G., & Zuxing, X. (2017). A new approach for ranking fuzzy numbers based on possibility theory. Journal of Computational and Applied Mathematics, 309, 674-682.] suggested a new fuzzy ranking technique on the basis of possibility theory. In this note, we show that this method leads to the incorrect result in various cases.

Critical path method plays an important role on managing medium to large-scale problems. It is often difficult to determine the critical path for different reasons such as the existing uncertainties in processing tasks. One alternative to handle the uncertainty associated with the processing time is to use fuzzy techniques. We present a new method to calculate the critical path method when the processing times follow trapezoidal fuzzy numbers. The proposed model of this paper does not use any defuzzification technique to find the final processing time. The implementation of the proposed model is compared with other techniques using a well-known example from the literature.

Analytic Hierarchy Process (AHP) is one of the most popular approaches in the area of multiple attribute decision making (MADM). However, it is not practical any more if input information are fuzzy. In this paper, we propose a new method for fuzzy AHP which is especially useful to make decisions for multiple attribute problems. The method is developed by applying preference ratio concept which makes it practical since it assigns crisp weights and crisp scores to different alternatives. Two algorithms are proposed in this paper: The first one defines crisp and normalized weight by pairwise comparison with fuzzy data while the second one calculates fuzzy consistency ratio. The proposed method is applied to prioritize different short courses in a management school.