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The intuitionistic linguistic variables are easier to describe the fuzzy information which widely exists in the real world, and Bonferroni mean can capture the interrelationship of the individual arguments. However, the traditional Bonferroni mean can only process the crisp number. In this paper, we will extend Bonferroni mean to the intuitionistic linguistic environment and propose a multiple attribute decision making method with intuitionistic linguistic information based on the extended Bonferroni mean which can consider the interrelationship of the attributes. Firstly, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic Bonferroni mean (ILBM) operator and an intuitionistic linguistic weighted Bonferroni mean (ILWBM) operator are developed, and some desirable characteristics of them are studied. At the same time, some special cases with respect to the parameters p and q in Bonferroni are analyzed. Based on the ILWBM operator, the approach to multiple attribute decision making with intuitionistic linguistic information is proposed. Finally, an illustrative example is given to verify the developed approach and to demonstrate its effectiveness.

Probabilistic linguistic Z number (PLZN) is considered as an effective information representation model. It not only describes the decision-making information, but also demonstrates its reliability. To handle the increasing problems of complexity and uncertainty in real-life, PLZN is widely used to indicate qualitative information. In this paper, a novel decision-making method with PLZNs is proposed, focusing on multiple attribute group decision-making (MAGDM) problems with fewer alternatives and more interacted attributes in PLZN environment. Firstly, all basic theories of PLZNs are shown, where the possibility degree of PLZNs is defined. Then, an integration model based on evidential reasoning theory is constructed to aggregate numerous PLZNs, which fully considers the incomplete probability distributions in PLZNs. The mathematical programming model with the generalized Shapley function is introduced to determinate the important degrees of attributes and reflect the interactive characteristics among them. In addition, the probabilistic linguistic Z QUALIFLEX (PLZ-QUALIFLEX) method with the generalized Shapley function is proposed to rank small numbers of alternatives with respect to large numbers of attributes with heterogeneous relationships. Lastly, after demonstrating the rationalities and superiorities of the proposed method, it is applied to solve some numerical cases, in which is compared with other methods. [ABSTRACT FROM AUTHOR]

This paper demonstrates that transportation networks may be used to assess and predict the regional risk of COVID-19 infection from the outbreak. We use China's high-speed rail (HSR) network at the scale of prefecture level to assess, based on a probabilistic risk model, the risk of COVID-19 infection from Wuhan to the country's 31 province-level regions at the early stage of domestic spread. We find that the high-risk regions are mainly distributed along the southern half of Beijing-Hong Kong HSR line, where a large number of infection cases have been confirmed at the early stage. Furthermore, the two components of the infection risk, namely, the probability (proxied by the region's correlation with Wuhan through HSR) and the impact (proxied by the region's population with mobility), can play different roles in the risk ranking for different regions. For public health administrators, these findings may be used for better decision making, including the preparation of emergency plans and supplies, and the allocation of limited resources, before the extensive spread of the epidemic. Moreover, the administrators should adopt different intervention measures for different regions, so as to better mitigate the epidemic spread according to their own risk scenarios with respect to the probability of occurring and, once occurred, the impact. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy numbers (FNs), which add an abstinence degree based on membership and non-membership degrees, can express neutral information conveniently and have a considerable large range of information expression. The normal FNs (NFNs) are very available to characterize normal distribution phenomenon widely existing in social life. In this paper, we first define the normal T-SFNs (NT-SFNs) which can combine the advantages of T-SFNs and NFNs. Then, we define their operational laws, score value, and accuracy value. By considering the interrelationship among multi-input parameters, we propose the Maclaurin symmetric mean operator with NT-SFNs (NT-SFMSM) and its weighted form (NT-SFWMSM). Furthermore, we study some characteristics and special cases of them. Based on the NT-SFWMSM operator, we put forward a novel multi-attribute decision-making (MADM) approach. Finally, some numerical examples are conducted to prove that the proposed approach is valid and superior to some other existing methods. [ABSTRACT FROM AUTHOR]

As the development and extension of hesitant fuzzy linguistic term sets (HFLTSs), free double hierarchy hesitant fuzzy linguistic term sets (FDHHFLTSs) can describe the evaluation information in more detail. In addition, in practical multiple attribute decision-making (MADM) problems, priority relations and interaction relations usually exist among attributes, and the prioritized interactive Choquet (PIC) operator based on generalized prioritized measure-guided aggregation (GPMGA) operator and Choquet integral (CI) operator is an effective tool for dealing with decision-making problems with priority relations and interaction relations. Under the above contexts, we improve the PIC operator and propose the FDHHFLPIC operator which can aggregate the evaluation information under free double hesitant fuzzy linguistic environment and take both priority and interaction relations into account. Furthermore, we propose an approach based on the FDHHFLPIC operators to address the real MADM problem, and the proposed method considering the different relations between attributes in decision-making process. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed method which can consider priority relations and interaction relations under the FDHHFLTSs. [ABSTRACT FROM AUTHOR]