A Novel Integration Method for D Numbers Based on Horizontal Comparison

D numbers theory is an extension of Dempster–Shafer evidence theory. It eliminates the constraints of mutual exclusion and completeness under the frame of discernment of Dempster–Shafer evidence theory, so it has been widely used to deal with uncertainty modelling, but if it cannot effectively deal with the problem of missing information, sometimes unreasonable conclusions will be drawn. This paper proposes a new type of integration representation of D numbers, which compares the data of multiple evaluation items horizontally, and can reasonably fill in missing information. We apply this method to the user experience evaluation problem of online live course platform to verify the effectiveness of this method.

D NUMBERS – FUCOM – FUZZY RAFSI MODEL FOR SELECTING THE GROUP OF CONSTRUCTION MACHINES FOR ENABLING MOBILITY

The paper presents a hybrid model for decision-making support based on D numbers, the FUCOM method and fuzzified RAFSI method, used for solving the selection of the group of construction machines for enabling mobility. By applying D numbers, the input parameters for the calculation of the weight coefficients of the criteria were provided. The calculation of the weight coefficients of the criteria was performed using the FUCOM method. The best alternative was selected using the fuzzified method, which was conditioned by the specificity of the issue so that in this case, the selection of the best alternative was made using the fuzzified RAFSI method.

An integrated FMEA approach using Best-Worst and MARCOS methods based on D numbers for prioritization of failures

Failure modes and effects analysis (FMEA) is a useful reliability analysis technique to identify potential failure modes in a wide range of industries. However, the conventional FMEA method is deficient in dealing with the risk evaluation and prioritization method. To overcome the shortcomings, this paper presents a new risk priority model using Best-Worst Method based on D numbers (D-BWM) and the Measurement of Alternatives and Ranking according to COmpromise Solution based on D numbers (D-MARCOS). First, D numbers are used to deal with the uncertainty of FMEA team members’ subjective judgment. Second, the distance-based method is proposed to determine the objective weight of each team member. Then, the D-BWM was used to determine the weight of risk factors. The combination rule of D number theory combined the evaluation information of multiple members into group opinions. Finally, D-MARCOS method is proposed to obtain the risk priority of the failure modes. An example and the results of comparative analysis show the method is effective.

MADA problem: A new scheme based on D numbers and aggregation functions

Describing and processing complex as well as ambiguous and uncertain information has always been an inescapable and challenging topic in multi-attribute decision analysis (MADA) problems. As an extension of Dempster-Shafer (D-S) evidence theory, D numbers breaks through the constraints of the constraint framework and is a new way of expressing uncertainty. The soft likelihood function based on POWA operator is one of the most useful tools recently developed for dealing with uncertain information, since it provides a more excellent performance for the aggregation of multiple compatible evidence. Recently, a new MADA model based on D numbers has been proposed, called DMADA. In this paper, inspired by the above mentioned theories, based on soft likelihood functions, POWA aggregation and D numbers we design a novel model to improve the performance of representing and processing uncertain information in MADA problems as an improvement of the DMADA approach. In contrast, our advantages include mainly the following. Firstly, the proposed method considers the reliability characteristics of each initial D number information. Secondly, the proposed method empowers decision makers with the possibility to express their perceptions through attitudinal features. In addition, an interesting finding is that the preference parameter in the proposed method can clearly distinguish the variability between candidates by adjusting the space values between adjacent alternatives, making the decision results clearer. Finally, the effectiveness and superiority of this model are proved through analysis and testing.

Colonization of Trees by Ambrosia Beetles (Coleoptera: Curculionidae: Scolytinae) Is Influenced by Duration of Flood Stress

The ambrosia beetles Xylosandrus germanus (Blandford) and Xylosandrus crassiusculus (Motschulsky) bore into flood-stressed trees to establish colonies, but the influence of flooding duration on colonization is unknown. This relationship was examined by flooding trees for various time periods and evaluating colonization. In one experiment, X. germanus bored into 20 dogwood (Cornus florida L.) trees during a 3-d flood treatment. Ten trees dissected that season had no offspring present in tunnels; the remaining trees appeared healthy and bloomed the following spring. In another experiment, dogwood trees were flooded for 3 or 7 d and then dissected to assess colonization. The incidence of superficial (short unbranched) and healed (callus tissue in entrance) tunnels was greater in the 3-d trees, while the incidence of tunnels with X. germanus or offspring was greater in the 7-d trees. Four experiments (three in Ohio and one in Virginia) had flood treatments of 0 (nonflooded), 3, 5, 7, and 10 d. Numbers of tunnel entrances, tunnels with X. germanus, and incidence of tunnels with offspring or live foundresses tended to increase as flood duration increased on apple (Malus × domestica Borkh.), dogwood, and redbud (Cercis canadensis L.) in Ohio and redbud in Virginia. Nonflooded trees in Ohio had no boring activity, but ambrosia beetles bored into three nonflooded trees in Virginia. Indicators of unsuccessful colonization, such as superficial tunnels and healing, decreased as flood duration increased. These results suggest tree crops may recover from boring by ambrosia beetles following short-duration flood events, and not necessarily require culling.

Distance Metrics of D Numbers

Belief function has always played an indispensable role in modeling cognitive uncertainty. As an inherited version, the theory of D numbers has been proposed and developed in a more efficient and robust way. Within the framework of D number theory, two more generalized properties are extended: (1) the elements in the frame of discernment (FOD) of D numbers do not required to be mutually exclusive strictly; (2) the completeness constraint is released. The investigation shows that the distance function is very significant in measuring the difference between two D numbers, especially in information fusion and decision. Modeling methods of uncertainty that incorporate D numbers have become increasingly popular, however, very few approaches have tackled the challenges of distance metrics. In this study, the distance measure of two D numbers is presented in cases, including complete information, incomplete information, and non-exclusive elements