NEW RESULTS ON THE EXISTING FUZZY DISTANCE MEASURES

Document Type : Research Paper

Authors

1 Department of Mathematics, Imam Khomeini International Uni- versity, Ghazvin, 34149-16818, Iran

2 Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran

Abstract

In this paper, we investigate the properties of some recently pro-
posed fuzzy distance measures. We find out some shortcomings for these dis-
tances and then the obtained results are illustrated by solving several examples
and compared with the other fuzzy distances.

Keywords


[1] S. Abbasbandy and M. Amirfakhrian, The nearest trapezoidal form of a generalized left right
fuzzy number, Internat. J. Approx. Reason., 170 (2006), 166-178.
[2] S. Abbasbandy and T. Hajjari, Weighted trapezoidal approximation-preserving cores of a
fuzzy number, Comput. Math. Appl., 59 (2010), 3066-3077.
[3] A. I. Ban, On the nearest parametric approximation of a fuzzy number-revisited, Fuzzy Sets
and Systems, 160 (2009), 3027-3047.
[4] A. I. Ban, Triangular and parametric approximations of fuzzy numbers-inadvertences and
corrections, Fuzzy Sets and Systems, 160 (2009), 3048-3058.
[5] K. M. Bjork, An analytical solution to a fuzzy economic order quantity problem, Internat. J.
Approx. Reason., 50 (2009), 485-493.
[6] C. Chakraborty and D. Chakraborty, A theoretical development on a fuzzy distance measure
for fuzzy numbers, Math. Compu. Modelling, 43 (2006), 254-261.
[7] C. H. Cheng, A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and
Systems, 95 (1998), 307-317.
[8] P. Diamond, Fuzzy least squares, Information Sciences, 46 (1988), 41-157.
[9] D. Guha and D. Chakraborty, A new approach to fuzzy distance measure and similarity
measure between two generalized fuzzy numbers, Appl. Soft Comput., 10 (2010), 90-99.
[10] J. Kacprzyk, Multistage Fuzzy Control, Wiley, Chichester, 1997.
[11] A. Maturo, On some structures of fuzzy numbers, Iranian Journal of Fuzzy Systems, 6(4)
(2009), 49-59.
[12] E. Pasha, A. Saiedifar and B. Asady, The percentiles of fuzzy numbers and their applications,
Iranian Journal of Fuzzy Systems, 6(1) (2009), 27-44.
[13] R. O. Rodrguez, F. Esteva, P. Garcia and L. Godo, On implicative closure operators in
approximate reasoning, Int. J. Approximate Reasoning, 33 (2003), 159{184.
[14] L. Tran and L. Duckstein, Comparison of fuzzy numbers using a fuzzy distance measure,
Fuzzy Sets and Systems, 130 (2002), 331-341.
[15] T. Vijayan and M. Kumaran, Fuzzy economic order time models with random demand, In-
ternat. J. Approx. Reason., 50 (2009), 529-540.
[16] W. Voxman, Some remarks on distances between fuzzy numbers, Fuzzy Sets and Systems,
100 (1998), 353-365.
[17] R. Xu and C. Li, Multidimensional least-squares tting with a fuzzy model, Fuzzy Sets and
Systems, 119 (2001), 215-223.
[18] M. S. Yang and C. H. Ko, On cluster-wise fuzzy regression analysis, IEEE Transactions on
Systems, Man and Cybernetics Part B, 27 (1997), 1-13.