A New Approach for Ranking of L-R Type Generalized Fuzzy Numbers

10.6988/TOJIMS.201105.0197

Amit Kumar；Pushpinder Singh；Parmpreet Kaur；Amarpreet Kaur

Ranking function ； L-R type generalized fuzzy number

Tamsui Oxford Journal of Information and Mathematical Sciences

27卷2期（2011 / 05 / 01）

197 - 211

英文

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 (A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems 95 (1998) 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 (Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems 50 (1992) 247-255) is not ture. 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 the results proposed by Chen and Chen (Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications 36 (2009) 6833-6842) are not accurate. 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.