A New Centroids Method for Ranking of Trapezoid Fuzzy Numbers
DOI:
https://doi.org/10.11113/jt.v68.1124Keywords:
Centroid of trapezoid, ranking fuzzy numbers, circumcenter, centroid of triangle, centroid of rectangleAbstract
Ranking fuzzy numbers has become an important process in decision making. Many ranking methods have been proposed thus far and one of the commonly used is centroid of trapezoid. However, there is still no agreement on the method that can always provide a satisfactory solution to every situation. This paper aims to propose a new method of centroid using the circumcenter. The calculation for the circumcenter is derived from the trapezoidal fuzzy numbers and a series of the proposed steps. The proposed method offers a straightforward calculation by considering the centroid in each part of trapezoid to obtain a new centroid which eventually becomes the circumcenter. The Euclidean distance is used to calculate the ranking function from the circumcenter of centroids and the original point. A numerical example is given to illustrate the proposed method. At the end of this paper, a comparison of centroid method between the proposed method and other methods is presented.
References
Chen, S. J. and C. L. Hwang. 1992. Fuzzy Multiple Attribute Decision Making, Methods and Applications. Berlin: Springer.
Lee, J. H. and K. H. You. 2003. A Fuzzy Ranking Method for Fuzzy Numbers. IEICE Trans Fundam Electrom Commun Comput Sci. E86-A(10): 2650–2658.
Rao, P. P. B. and N. R. Shankar. 2011. Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and Index of Modality. Advances in Fuzzy Systems.
Jain, R. 1976. Decision-making in the Presence of Fuzzy Variables. IEEE Transactions on Systems, Man. and Cybernatics. 6(10): 698–703.
Bortolan, G. and R. Degani. 1985. A Review of Some Methods for Ranking Fuzzy Subsets. Fuzzy Sets and Systems. 15(1): 1–19.
Chen, S. H. 1985. Ranking Fuzzy Numbers with Maximizing Set and Minimizing Set. Fuzzy Sets and Systems. 17(2): 113–129.
Delgado, M., J. L. Verdegay and M. A. Vila. 1988. A Procedure for Ranking Fuzzy Numbers Using Fuzzy Relations. Fuzzy Sets and Systems. 26(1): 49–62.
Kim, K. and K. S. Park. 1990. Ranking Fuzzy Numbers with Index of Optimism. Fuzzy Sets and Systems. 35(2): 143–150.
Yuan, Y. 1991. Criteria for Evaluating Fuzzy Ranking Methods. Fuzzy Sets and Systems. 43(2): 139–157.
Choobineh, F. and H. Li. 1993. An Index for Ordering Fuzzy Numbers. Fuzzy Sets and Systems. 54(3): 287–294.
Cheng, C.H. 1998. A New Approach for Ranking Fuzzy Numbers by Distance Method. Fuzzy Sets and Systems. 95(3): 307–317.
Chen, L. H. and H. W. Lu. 2001. An Approximate Approach for Ranking Fuzzy Numbers Based on Left and Right Dominance. Computers and Mathematics with Applications. 41(12): 1589–1602.
Deng, Y., Z. Zhenfu and L. Qi. 2006. Ranking Fuzzy Numbers with an Area Method Using Radius of Gyration. Computers and Mathematics with Applications. 51(6–7): 1127–1136.
Nejad, A. M. and M. Mashinchi. 2010. Ranking Fuzzy Numbers Based on The Areas on The Left and The Right Sides of Fuzzy Number. Computers and Mathematics with Applications. 61(2): 431–442.
Yager, R. R. 1981. Fuzzy Decision Making Including Unequal Objectives. Fuzzy Sets and Systems. 1(2): 87–95.
Chu, T. C. and C. T. Tsao. 2002. Ranking Fuzzy Numbers with an Area between the Centroid Point and Original Point. Computers and Mathematics with Applications. 43(1): 111–117.
Liang, C., J. Wu and J. Zhang. 2006. Ranking Indices and Rules for Fuzzy Numbers Based on Gravity Center Point. Intelligent Control and Automation. 1: 3159–3163.
Wang, Y. J. and H. S. Lee. 2008. The Revised Method of Ranking Fuzzy Numbers with an Area between the Centroid and Original Points. Computers and Mathematics with Applications. 55: 2033–2042.
Lian, Z., B. Jiao and X. Gu. 2006. A Novel Method of Ranking Fuzzy Numbers for Decision-making Problems. Intelligent Systems Design and Application. 1: 354–360.
Kaufmann, A. and M. M. Gupta. 1988. Fuzzy Mathematical Models in Engineering and Management Science. Amsterdam: North-Holland.
Loy, J. 2011. The Centers of Triangle. http://www.jimloy.com/geometry/centers.htm. Retrieved on 12 March 2012.
Goetschel, R. and W. Voxman. 1986. Elementary Fuzzy Calculus. Fuzzy Sets and Systems. 18(1): 31–43.
Chen, S.H.. 1999. Ranking Generalized Fuzzy Number with Graded Mean Integration. Proceedings of the Eighth International Fuzzy Systems Association World Congress. 2:899–902.
Chen, S.J. and S.M. Chen. 2007. Fuzzy Risk Analysis Based on the Ranking of Generalized Trapezoidal Fuzzy Numbers. Applied Intelligence. 26(1): 1–11.
Abbasbandy, S. and T. Hajjari. 2009. A New Approach for Ranking of Trapezoidal Fuzzy Numbers. Computers and Mathematics with Applications. 57(3): 413–419.
Chen, S.M. and J.H. Chen. 2009. Fuzzy Risk Analysis Based on Ranking Generalized Fuzzy Numbers with Different Heights and Different Spreads. Expert Systems with Applications. 36(3): 6833–6842.
Kumar, A., P. Singh, A. Kaur and P. Kaur. 2010. Ranking of Generalized Trapezoidal Fuzzy Numbers Based on Rank, Mode, Divergence and Spread. Turkish Journal of Fuzzy Systems. 1(2): 141–152.
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