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**A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making.**
*(English)*
Zbl 1311.68156

Summary: The ranking of interval-valued intuitionistic fuzzy sets (IVIFSs) is very important for the interval-valued intuitionistic fuzzy decision making. From the probability viewpoint, the possibility degree of comparison between two interval-valued intuitionistic fuzzy numbers (IVIFNs) is defined by using the notion of 2-dimensional random vector, and a new method is then developed to rank IVIFNs. Hereby the ordered weighted average operator and hybrid weighted average operator for IVIFNs are defined based on the Karnik-Mendel algorithms and employed to solve multi-attribute group decision making problems with IVIFNs. The individual overall attribute values of alternatives are obtained by using the weighted average operator for IVIFNs. By using the hybrid weighted average operator for IVIFNs, we can obtain the collective overall attribute values of alternatives, which are used to rank the alternatives. A numerical example is examined to illustrate the effectiveness and flexibility of the proposed method in this paper.

### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

91B06 | Decision theory |

### Keywords:

multi-attribute group decision making; interval-valued intuitionistic fuzzy set; aggregation operator; Karnik-Mendel algorithms
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\textit{S. Wan} and \textit{J. Dong}, J. Comput. Syst. Sci. 80, No. 1, 237--256 (2014; Zbl 1311.68156)

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