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The 2-tuple linguistic neutrosophic set (2TLNS) does a good job in coping with vague and uncertain environments and has been widely used in numerous fields. In this article, we come up with a new solution of mul

Network security is a very important issue in recent years. For many new or traditional enterprises, utilizing internet to store and analyze data has become an indivisible part of their production and operation. But many enterprises do not have enough ability to ensure the security of information, so the choice of the optimal network security service provider has become a practical problem faced by many ordinary companies. In this paper, we establish bipolar fuzzy interactive multi‐criteria decision‐making (TODIM) based on the cumulative prospect theory (CPT‐TODIM) model for dealing with the problem of multi‐attribute group decision making, and this special model is applied to the field of network security about the issue of network security service provider selection. The second and third parts of this paper introduce the knowledge of bipolar fuzzy and the initial CPT‐TODIM method. In the fourth part, we discuss the bipolar fuzzy CPT‐TODIM model in detail. In the last two parts of this article, the method proposed in this paper is applied to the field of network security provider selection and compared with other methods. The results show that bipolar fuzzy CPT‐TODIM method with unique advantages in some aspects is reasonable and effective, and can be applied to more uncertain decision fields. It is hoped that this method can help enterprises make better decisions.

The urban ecological risk assessment is a new research field, which has been rising and developing with the change of environment management objectives and environment conception. The urban ecological risk assessment could be regarded as a classical Multi-attribute group decision making (MAGDM) issue. The interval-valued intuitionistic fuzzy set (IVIFS) can fully describe the uncertain information for the urban ecological risk assessment. Furthermore, the classical TODIM (an acronym in Portuguese for Interactive Multi-Criteria Decision Making) is built on cumulative prospect theory (CPT), which is a selectable method in reflecting the DMs’ psychological behavior. Thus, in this paper, the TODIM method based on the CPT is proposed for MAGDM issue under IVIFS. At the same time, it is enhancing rationality to get the weight information of attributes by using the interval-valued intuitionistic fuzzy entropy weight method. And focusing on hot issues in contemporary society, this article applies the discussed method to urban ecological risk assessment, and demonstrates urban ecological risk assessment model based on the proposed method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable.