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Fuzzified Choquet Integral and its Applications in MADM: A Review and A New Method

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Abstract

Aggregation of information using Choquet integral method, caused to interdependent or interactive characteristics among the decision maker’s preference criteria also considered. In this paper, after introducing Choquet integral as a powerful aggregation function, some existing fuzzified Choquet integral methods will be reviewed. Then, we propose a new method for aggregation of fuzzy-valued information using Choquet integral and compare it with others. This method preserves the properties of fuzzy numbers, that is, the resulting data are the same type as the early data. So, ranking of such numbers, which is necessary in multi attribute decision-making (MADM) problems, was performed using ranking methods of fuzzy numbers. Also, we will apply the proposed method in both single and group decision-making problems to solve MADM problems, while the evaluation values and then decision matrix are fuzzy numbers.

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Notes

  1. In [40] it is called α-cut of fuzzy-valued function, but it may be considered as α-cut of fuzzy set wrongly, then we called it α-level set as in Definition 3.1.

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Acknowledgments

The authors would like to thank the associate editor and the anonymous reviewers whose comments are quite useful for us to improve the paper.

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  1. Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    A. Keikha & H. Mishmast Nehi

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Keikha, A., Mishmast Nehi, H. Fuzzified Choquet Integral and its Applications in MADM: A Review and A New Method. Int. J. Fuzzy Syst. 17, 337–352 (2015). https://doi.org/10.1007/s40815-015-0037-0

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