Abstract

The last few decades have seen a large number of methods for ranking fuzzy numbers; centroid-index based approaches are the most commonly used among them. However, there are some weaknesses associated with these centroid-indices. Therefore, this paper reviews several fuzzy numbers ranking methods based on centroid-indices and proposes a new centroid-index ranking method that is capable of effectively ranking various types of fuzzy numbers. The proposed centroid-index ranking method uses fuzzy TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to solve multi-criteria decision making (MCDM) problems, where triangular fuzzy numbers express the ratings of each alternative and importance weight of each criterion. To avoid complicated calculations of fuzzy numbers, the normalized weighted ratings are defuzzified into crisp values to simplify the calculations of distances from each alternative to the ideal and to the negative ideal solutions. A closeness coefficient is defined to determine the ranking order of alternatives. The proposed method is applied to a parting surface evaluation and selection problem in plastic mold design, demonstrating its applicability and computational process.

Key words: Ranking fuzzy numbers, centroid index, fuzzy TOPSIS, parting surface.