A new method for ordering triangular fuzzy numbers
Subject Areas : Operation Research
1 -
2 - Department of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, Japan
Keywords: Linear order, ranking fuzzy numbers, triangular fuzzy number,
Abstract :
Ranking fuzzy numbers plays a very important role in linguistic decision making and other fuzzy application systems. In spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. Shortcoming are found in some of the convenient methods for ranking triangular fuzzy numbers such as the coefficient of variation (CV index), distance between fuzzy sets, centroid point and original point, and also weighted mean value. In this paper, we introduce a new method for ranking triangular fuzzy number to overcome the shortcomings of the previous techniques. Finally, we compare our method with some convenient methods for ranking fuzzy numbers to illustrate the advantage our method.
[1] Abbasbandy S., and Asady B., Ranking of fuzzy numbers by sign distance, Information Sciences, 176, 2405-2416, 2006.
[2] Asady B., and Zendehnam A., Ranking fuzzy numbers by distance minimization, Applied Mathematical Modeling, 31, 2589-2598, 2007.
[3] Bortolan G., and Degani R., A review of some methods for ranking numbers, Fuzzy Sets and Systems, 15, 1-19, 1985.
[4] Chen S.H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, 17, 113-129, 1985.
[5] Chen L.H., and Lu H.W., An approximate approach for ranking fuzzy numbers based on left and right dominance, Comput. Math. Appl. 41, 1589-1602, 2001.
[6] Cheng C.H., A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 95, 307-317, 1998.
