A subjective approach for ranking fuzzy numbers
Fuzzy Sets and Systems
Ranking fuzzy numbers with integral value
Fuzzy Sets and Systems
A new approach for ranking fuzzy numbers by distance method
Fuzzy Sets and Systems
Reasonable properties for the ordering of fuzzy quantities (I)
Fuzzy Sets and Systems
Ranking fuzzy numbers by preference ratio
Fuzzy Sets and Systems
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers
Applied Intelligence
The revised method of ranking fuzzy numbers with an area between the centroid and original points
Computers & Mathematics with Applications
A new approach for ranking of trapezoidal fuzzy numbers
Computers & Mathematics with Applications
Expert Systems with Applications: An International Journal
A method for ranking fuzzy numbers and its application to decision-making
IEEE Transactions on Fuzzy Systems
Analyzing the ranking method for L-R fuzzy numbers based on deviation degree
Computers and Industrial Engineering
Engineering Applications of Artificial Intelligence
A type-2 linguistic set theory and its application to multi-criteria decision making
Computers and Industrial Engineering
Parting curve selection and evaluation using an extension of fuzzy MCDM approach
Applied Soft Computing
An improved ranking method for fuzzy numbers with integral values
Applied Soft Computing
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Hi-index | 12.05 |
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. Cheng (Cheng, C. H. (1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems, 95, 307-317) pointed out that the proof of the statement ''Ranking of generalized fuzzy numbers does not depend upon the height of fuzzy numbers'' stated by Liou and Wang (Liou, T. S., & Wang, M. J. (1992). Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems, 50, 247-255) is incorrect. In this paper, by giving an alternative proof it is proved that the above statement is correct. Also with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Chen, S. M., & Chen, J. H. (2009). Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications, 36, 6833-6842) is incorrect. The main aim of this paper is to modify the Liou and Wang approach for the ranking of L-R type generalized fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of generalized and normal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfy all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Wang, X., & Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems, 118, 375-385).