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Generalized Discrete Fuzzy Number and Application in Risk Evaluation

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Abstract

In this paper, the definition of generalized discrete fuzzy numbers is introduced, and a representation theorem of such fuzzy numbers is obtained. Based on the representation theorem, it is shown that the usual addition and multiplication which are defined by Zadeh’s extension principle do not preserve the closeness of the operation, and a new addition operation and a new multiplication operation are defined, which not only preserve the closeness of the operation, but also are easy to calculate. Then some weak orders on the generalized discrete fuzzy number space are defined, and their properties are investigated. At last, a practical example is given to show the application of the algorithmic version to rank uncertain or imprecise discrete quantity.

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Acknowledgments

This work was partially supported by the Nature Science Foundation of China (Nos. 61273077 and 61433001), the Nature Science Foundation of Zhejiang Province, China (No. LY12A01001).

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Authors and Affiliations

  1. Institute of Operations Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, 310018, China

    Guixiang Wang & Junxia Wang

Authors
  1. Guixiang Wang
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  2. Junxia Wang
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Correspondence to Guixiang Wang.

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Wang, G., Wang, J. Generalized Discrete Fuzzy Number and Application in Risk Evaluation. Int. J. Fuzzy Syst. 17, 531–543 (2015). https://doi.org/10.1007/s40815-015-0038-z

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  • DOI: https://doi.org/10.1007/s40815-015-0038-z

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