-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variables and .
References
H. Kwakernaak, “Fuzzy random variables. I. Definitions and theorems,” Information Sciences, vol. 15, no. 1, pp. 1–29, 1978. MR538672 0438.60004 10.1016/0020-0255(78)90019-1 H. Kwakernaak, “Fuzzy random variables. I. Definitions and theorems,” Information Sciences, vol. 15, no. 1, pp. 1–29, 1978. MR538672 0438.60004 10.1016/0020-0255(78)90019-1
M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986. MR833596 0592.60004 10.1016/0022-247X(86)90093-4 M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986. MR833596 0592.60004 10.1016/0022-247X(86)90093-4
J. M. Ruiz and J. Navarro, “Characterization of distributions by relationships between failure rate and mean residual life,” IEEE Transactions on Reliability, vol. 43, no. 4, pp. 640–644, 1994. J. M. Ruiz and J. Navarro, “Characterization of distributions by relationships between failure rate and mean residual life,” IEEE Transactions on Reliability, vol. 43, no. 4, pp. 640–644, 1994.
R. C. Gupta, “On the mean residual life function in survival studies,” in Statistical Distribution in Scientific works, C. Tailie, G. P. Patil, and B. A. Baldessar, Eds., vol. 79 of NATO Advanced study Institutes Series, pp. 327–334, Reidel, Dordrecht, The Netherlands, 1981. MR656346 R. C. Gupta, “On the mean residual life function in survival studies,” in Statistical Distribution in Scientific works, C. Tailie, G. P. Patil, and B. A. Baldessar, Eds., vol. 79 of NATO Advanced study Institutes Series, pp. 327–334, Reidel, Dordrecht, The Netherlands, 1981. MR656346
R. C. Gupta and H. Olcay Akman, “Mean residual life function for certain types of non-monotonic ageing,” Communications in Statistics. Stochastic Models, vol. 11, no. 1, pp. 219–225, 1995. MR1316777 10.1080/15326349508807340 0813.60081 R. C. Gupta and H. Olcay Akman, “Mean residual life function for certain types of non-monotonic ageing,” Communications in Statistics. Stochastic Models, vol. 11, no. 1, pp. 219–225, 1995. MR1316777 10.1080/15326349508807340 0813.60081
M. S. Finkelstein, “On the shape of the mean residual lifetime function,” Applied Stochastic Models in Business and Industry, vol. 18, no. 2, pp. 135–146, 2002. MR1907353 1007.62084 10.1002/asmb.461 M. S. Finkelstein, “On the shape of the mean residual lifetime function,” Applied Stochastic Models in Business and Industry, vol. 18, no. 2, pp. 135–146, 2002. MR1907353 1007.62084 10.1002/asmb.461
M. G. H. Akbari, A. H. Rezaei, and Y. Waghei, “Statistical inference about the variance of fuzzy random variables,” The Indian Journal of Statistics B, vol. 71, no. 2, pp. 206–221, 2009. MR2639304 1192.60010 M. G. H. Akbari, A. H. Rezaei, and Y. Waghei, “Statistical inference about the variance of fuzzy random variables,” The Indian Journal of Statistics B, vol. 71, no. 2, pp. 206–221, 2009. MR2639304 1192.60010
J. G. Shanthikumar and D. D. Yao, “Bivariate characterization of some stochastic order relations,” Advances in Applied Probability, vol. 23, no. 3, pp. 642–659, 1991. MR1122880 0745.62054 10.1017/S0001867800023788 J. G. Shanthikumar and D. D. Yao, “Bivariate characterization of some stochastic order relations,” Advances in Applied Probability, vol. 23, no. 3, pp. 642–659, 1991. MR1122880 0745.62054 10.1017/S0001867800023788
T. Itoh and H. Ishii, “One machine scheduling problem with fuzzy random due-dates,” Fuzzy Optimization and Decision Making, vol. 4, no. 1, pp. 71–78, 2005. MR2127798 1079.90054 10.1007/s10700-004-5571-4 T. Itoh and H. Ishii, “One machine scheduling problem with fuzzy random due-dates,” Fuzzy Optimization and Decision Making, vol. 4, no. 1, pp. 71–78, 2005. MR2127798 1079.90054 10.1007/s10700-004-5571-4
J. E. L. Piriyakumar and S. Ramasubramanian, “Bivariate characterization of stochastic orderings of fuzzy random variables,” in Proceedings of the International Conference in Management Sciences and Decision Making, pp. 25–31, Tamkang University, Taipei, Taiwan, 2010. J. E. L. Piriyakumar and S. Ramasubramanian, “Bivariate characterization of stochastic orderings of fuzzy random variables,” in Proceedings of the International Conference in Management Sciences and Decision Making, pp. 25–31, Tamkang University, Taipei, Taiwan, 2010.
G.-Y. Wang and Y. Zhang, “The theory of fuzzy stochastic processes,” Fuzzy Sets and Systems, vol. 51, no. 2, pp. 161–178, 1992. MR1188308 10.1016/0165-0114(92)90189-B 0782.60039 G.-Y. Wang and Y. Zhang, “The theory of fuzzy stochastic processes,” Fuzzy Sets and Systems, vol. 51, no. 2, pp. 161–178, 1992. MR1188308 10.1016/0165-0114(92)90189-B 0782.60039
H.-C. Wu, “Probability density functions of fuzzy random variables,” Fuzzy Sets and Systems, vol. 105, no. 1, pp. 139–158, 1999. \endinput MR1688002 0936.60001 10.1016/S0165-0114(97)00241-8 H.-C. Wu, “Probability density functions of fuzzy random variables,” Fuzzy Sets and Systems, vol. 105, no. 1, pp. 139–158, 1999. \endinput MR1688002 0936.60001 10.1016/S0165-0114(97)00241-8
