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On weighted lower and upper possibilistic means and variances of fuzzy numbers and its application in decision

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Abstract

In this paper, we define the weighted lower and upper possibilistic variances and covariances of fuzzy numbers. We also obtain their many properties similar to variance and covariance in probability theory. On the basis of the weighted lower and upper possibilistic means and variances, we present two new possibilistic portfolio selection models with tolerated risk level and holdings of assets constraints. The conventional probabilistic mean–variance model can be transformed to a linear programming problem under possibility distributions. Finally, an estimation method of possibility distribution is offered and a real example for portfolio selection problem is given to illustrate the usability of the approach and the effectiveness of our methods.

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Authors and Affiliations

  1. School of Business Administration, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Wei-Guo Zhang & Wei-Lin Xiao

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  1. Wei-Guo Zhang
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  2. Wei-Lin Xiao
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Correspondence to Wei-Guo Zhang.

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Zhang, WG., Xiao, WL. On weighted lower and upper possibilistic means and variances of fuzzy numbers and its application in decision. Knowl Inf Syst 18, 311–330 (2009). https://doi.org/10.1007/s10115-008-0133-7

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  • DOI: https://doi.org/10.1007/s10115-008-0133-7

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