The new weighted magnitude mean value and variance of fuzzy numbers

Fuller and Majlender ( Fuzzy Sets and Systems 136 (2003) 363-374) introduced the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-valued probabilistic mean. In this paper, we introduce the new notation of lower and upper weighted magnitude mean values of a fuzzy number. The new interval-valued weighted magnitude mean and variance are defined, which differs from the one given by Fuller and Majlender. We will show the relationship of interval- valued weighted magnitude mean and interval-valued weighted possibilistic mean. Furthermore, we shall also introduce the notations of crisp weighted magnitude mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. Finally, some comparative examples are used to illustrate the advantage of the proposed weighted magnitude mean value and variance method to order fuzzy numbers.