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A New Magnitude Possibilistic Mean Value and Variance of Fuzzy Numbers

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Abstract

Carlsson and Fullér (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 Fullér. 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.

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Acknowledgments

The author is very grateful to the respected editor and the anonymous reviewers for their constructive comments and suggestions that have led to an improved version of this paper. The work was supported in part by the Natural Science Foundation of Jiangsu Province of China (Nos. BK20130242, BK20131135) and the National Nature Science Foundation of China (No. 71303074).

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Authors and Affiliations

  1. Department of Information Management, Hohai University, Changzhou, China

    Gong Yanbing, Hu Na & Liu Gaofeng

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  1. Gong Yanbing
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  2. Hu Na
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  3. Liu Gaofeng
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Correspondence to Gong Yanbing.

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Yanbing, G., Na, H. & Gaofeng, L. A New Magnitude Possibilistic Mean Value and Variance of Fuzzy Numbers. Int. J. Fuzzy Syst. 18, 140–150 (2016). https://doi.org/10.1007/s40815-015-0072-x

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  • DOI: https://doi.org/10.1007/s40815-015-0072-x

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