A New Magnitude Possibilistic Mean Value and Variance of Fuzzy Numbers

作者：Gong Yanbing^*; Hu Na; Liu Gaofeng

来源：International Journal of Fuzzy Systems, 2016, 18(1): 140-150.

DOI：10.1007/s40815-015-0072-x

• Fuzzy numbers
• Magnitude possibilistic mean
• Magnitude possibilistic variance

Carlsson and Full,r (Fuzzy Sets Syst 122: 315-326, 2001) introduced the notations of lower possibilistic and upper possibilistic mean values of a fuzzy number, and investigated its relationship to the interval-valued possibilistic mean and variance. In this paper, we introduce the new notations of lower magnitude and upper magnitude mean values of a fuzzy number. The new interval-valued magnitude mean and variance are defined, which differs from the one given by Carlsson and Full,r. The relationship between the interval-valued magnitude mean and the interval-valued possibilistic mean is investigated. Furthermore, we shall also introduce the notations of crisp magnitude possibilistic 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 interval-valued magnitude possibilistic mean and variance method to ranking fuzzy numbers.

• 出版日期2016-2
• 单位河海大学