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An Attitudinal Nonlinear Integral and Applications in Decision Making

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Abstract

In the field of information fusion and decision making, integral is very common and important for aggregating a large variety of information. The integral to be used is usually nonlinear due to the nonadditive measure determined by the real world. In this study, we put forward a new nonlinear integral, which is first expressed as an interval, containing the infimum and supremum of the integrand on the nonadditive measure. Furthermore, an attitudinal nonlinear integral is defined by introducing the subjective attitude of the decision maker based on the integral interval obtained. A multi-criteria decision-making (MCDM) method considering the interaction between attribute features is developed based on the proposed attitudinal nonlinear integral and a case study is provided to demonstrate the usefulness of the decision-making method. Inspired by the golden rule representation, we define the generalized golden rule representative value of the interval integral and use it to solve the problem in the case study to illustrate its usefulness.

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Acknowledgements

We appreciate the encouragement of editors and anonymous reviewers. This research was funded by the grants from the National Natural Science Foundation of China (#71472053, #71429001, #91646105).

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  1. School of Management, Harbin Institute of Technology, 150001, Harbin, China

    Liguo Fei & Yuqiang Feng

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  1. Liguo Fei
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Correspondence to Liguo Fei.

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Fei, L., Feng, Y. An Attitudinal Nonlinear Integral and Applications in Decision Making. Int. J. Fuzzy Syst. 23, 564–572 (2021). https://doi.org/10.1007/s40815-020-00862-5

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