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Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making

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Abstract

Interval-valued intuitionistic fuzzy numbers (IVIFNs), which contain three ranges: the membership degree range, the non-membership degree range, and the hesitancy degree range, are very suitable to be used for depicting uncertain or fuzzy information. In this paper, we study the aggregation techniques of IVIFNs with the help of Frank operations. We first extend the Frank t-conorm and t-norm to interval-valued intuitionistic fuzzy environments and introduce several new operations of IVIFNs, such as Frank sum, Frank product, Frank scalar multiplication, and Frank exponentiation, based on which we develop several new interval-valued intuitionistic fuzzy aggregation operators, including the interval-valued intuitionistic fuzzy Frank weighted averaging operator and the interval-valued intuitionistic fuzzy Frank weighted geometric operator. We further establish various properties of these operators, give some special cases of them, and analyze the relationships between these operators. Moreover, we apply these operators to develop an approach for dealing with multiple attribute group decision making with interval-valued intuitionistic fuzzy information. Finally, a numerical example is provided to illustrate the practicality and effectiveness of the developed operators and approach.

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Acknowledgments

The author thanks the anonymous referees for their valuable suggestions in improving this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 61375075) and the Natural Science Foundation of Hebei Province of China (Grant No. F2012201020).

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  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, Hebei Province, People’s Republic of China

    Zhiming Zhang

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Zhang, Z. Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making. Neural Comput & Applic 28, 1471–1501 (2017). https://doi.org/10.1007/s00521-015-2143-1

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