An Improvement in Centroid Point Method for Ranking of Fuzzy Numbers

Introduction: In many applications, ranking of fuzzy numbers is an important component of the decision process. Many authors have investigated the use of fuzzy sets in ranking alternatives and they have studied different methods of raking fuzzy sets. Particularly, the ranking of fuzzy numbers. In a paper by Cheng [A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems 95 (1998) 307-317], a centroid-based distance method was suggested for ranking fuzzy numbers, both normal and non-normal. The method utilizes the Euclidean distances from the origin to the centroid point of each fuzzy numbers to compare and rank the fuzzy numbers. It is found that the mentioned method could not rank fuzzy numbers correctly. For example, it cannot rank fuzzy numbers when they have the same centroid point. Some other researches such as Chu and Tsao's , Wang and Lee and Deng et al. tried to overcome the shortcoming of the inconsistency of Cheng's method but their methods still have drawback. Aim: In this paper, we want to indicate these problems of Cheng's distance, Chu and Tsao's area and Wang and Lee's revised method and then we will propose an improvement method, which can avoid these problems for ranking fuzzy numbers. Materials and Methods: In point of our view, every fuzzy number may lead to zero, positive or negative real number. To overcome with this subject, we first introduce the sign function. By connecting the sign function, corrected centroid point formulas and Cheng’s distance method, the improvement method will be presented. Results: The proposed method includes all situations of fuzzy numbers to rank them correctly. Therefore, it improves the distance method of Cheng as well. Conclusion: In order to overcomes the shortcoming in Cheng's distance method, Chu and Tsao's formulae and new revised method by Wang and Lee, a sign function was introduced and composed an improvement strategy of Cheng’s distance. In this work those method are considered, which utilized the centroid points. The improved method can effectively rank various fuzzy numbers and their images. Thus, the method is superior to Cheng' distance, Chu and Tsao's area and Wang and Lee's revised method.