Interactive group decision making procedure based on uncertain multiplicative linguistic preference relations

Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express their linguistic preference information over alternatives.The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncertain multiplicative linguistic preference relations into a collective one,and then a simple approach is developed to determine the experts＇ weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference relations.Furthermore,a practical interactive procedure for group decision making is proposed based on uncertain multiplicative linguistic preference relations,in which a possibility degree formula and a complementary matrix are used to rank the given alternatives.Finally,the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.

Proof of Riemann Conjecture Based on Contradiction between Xi-Function and Its Product Expression

Riemann proved three results: analytically continue ζ(s) over the whole complex plane s =σ + it with a pole s =1;(Theorem A) functional equation ξ(t) = G(s0)ζ (s0), s0 =1/2 + it and (Theorem B) product expression ξ1(t) by all roots of ξ(t). He stated Riemann conjecture (RC): All roots of ξ (t) are real. We find a mistake of Riemann: he used the same notation ξ(t) in two theorems. Theorem B must contain complex roots;it conflicts with RC. Thus theorem B can only be used by contradiction. Our research can be completed on s0 =1/2 + it. Using all real roots rk and (true) complex roots zj = tj + iaj of ξ (z), define product expressions w(t), w(0) =ξ(0) and Q(t) > 0, Q(0) =1 respectively, so ξ1(t) = w(t)Q(t). Define infinite point-set L(ω) = {t : t ≥10 and |ζ(s0)| =ω} for small ω > 0. If ξ(t) has complex roots, then ω =ωQ(t) on L(ω). Finally in a large interval of the first module |z1|>>1, we can find many points t ∈ L(ω) to make Q(t) . This contraction proves RC. In addition, Riemann hypothesis (RH) ζ for also holds, but it cannot be proved by ζ.

Optimized interval 2-tuple linguistic aggregation operator based on PGSA and its application in MAGDM

This study proposes a multiple attribute group decisionmaking(MAGDM)approach on the basis of the plant growth simulation algorithm(PGSA)and interval 2-tuple weighted average operators for uncertain linguistic weighted aggregation(ULWA).We provide an example for illustration and verification and compare several aggregation operators to indicate the optimality of the assembly method.In addition,we present two comparisons to demonstrate the practicality and effectiveness of the proposed method.The method can be used not only to aggregate MAGDM problems but also to solve multi-granularity uncertain linguistic information.Its high reliability,easy programming,and high-speed calculation can improve the efficiency of ULWA characteristics.Finally,the proposed method has the exact characteristics for linguistic information processing and can effectively avoid information distortion and loss.

Solution to multiple attribute group decision making problems with two decision makers

A kind of multiple attribute group decision making （MAGDM） problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.

IDMA based MAI mitigation scheme with low complexity and low latency

High complexity and high latency are key problems for multiuser detection （MUD） to be applied to a mobile station in cellular networks. To tackle these problems, an interleave division multiple access （IDMA） based multiple access scheme, grouped spread IDMA （GSIDMA）, is proposed. In a GSIDMA system, lower complexity and latency for mobile stations can be achieved by appropriately dividing active users into different groups. The system model of GSIDMA is constructed and followed by analysing on its system capacity, complexity and latency, and bit error rate （BER） performance. The extrinsic information transfer （EXIT） chart is used to analyze the convergence behavior of the iteration process. The grouping method and interleavers-reuse issue for GSIDMA are also discussed preliminarily. The analyses and simulation results indicate that the complexity and latency of the proposed scheme are much lower than those of IDMA, whereas its BER performance is close to the latter. The properties of low complexity and low latency make it more feasible for the practical implementation.

Cells grouping scheme against pilot contamination in large scale antennas system

The influence of cells groupings factor to the performance of the cells groupings time-shift pilot scheme is researched for the multiple cells large scale antennas systems（LSAS）. The former researches have confirmed that the cells groupings time-shift pilots scheme is effective to reduce inter-cell interference, especially pilot contamination, which results from the pilot reuse in adjacent cells. However, they have not specified reasonable cells groupings factor, which plays a critical role in the general performance of the LSAS. Therefore, this problem is researched in details. The time for reverse-link data transmission will be compressed, when the groupings factor surpasses a certain range. Thus it is not always beneficial to increase the cells groupings factor without limitation. Furthermore,a reasonable cells groupings factor is deduced from the perspective of optimization to enhance the system performance. Simulations verify the proposed cell grouping factor.

Adaptively temporal graph convolution model for epidemic prediction of multiple age groups

Introduction:Multivariate time series prediction of infectious diseases is significant to public health,and the deep learning method has attracted increasing attention in this research field.Material and methods:An adaptively temporal graph convolution(ATGCN)model,which leams the contact patterns of multiple age groups in a graph-based approach,was proposed for COVID-19 and influenza prediction.We compared ATGCN with autoregressive models,deep sequence learning models,and experience-based ATGCN models in short-term and long-term prediction tasks.Results:Results showed that the ATGCN model performed better than the autoregressive models and the deep sequence learning models on two datasets in both short-term(12.5%and 10%improvements on RMSE)and longterm(12.4%and 5%improvements on RMSE)prediction tasks.And the RMSE of ATGCN predictions fluctuated least in different age groups of COVID-19(0.029±0.003)and influenza(0.059±0.008).Compared with the Ones-ATGCN model or the Pre-ATGCN model,the ATGCN model was more robust in performance,with RMSE of 0.0293 and 0.06 on two datasets when horizon is one.Discussion:Our research indicates a broad application prospect of deep learning in the field of infectious disease prediction.Transmission characteristics and domain knowledge of infectious diseases should be further applied to the design of deep learning models and feature selection.Conclusion:The ATGCN model addressed the multivariate time series forecasting in a graph-based deep learning approach and achieved robust prediction on the confirmed cases of multiple age groups,indicating its great potentials for exploring the implicit interactions of multivariate variables.

UNIFORMIZATION OF MULTIGRANULAR LINGUISTIC LABELS AND THEIR APPLICATION TO GROUP DECISION MAKING

In multiple attribute group decision making （MAGDM） problems based on linguistic information, the granularities of linguistic label sets are usually different due to the differences of thinking modes and habits among decision makers. In order to deal with this inconvenience, the transformation relationships among multigranular linguistic labels （TRMLLs）, which are applied to unify linguistic labels with different granularities into a certain linguistic label set with fixed granularity, are presented in this paper. Furthermore, the reference tables are made according to TRMLLs so that the interrelated calculation will be less complicated, and the method of how to use them is explained in detail. At length, the TRMLLs are illustrated through an application example.

Multivariate normal spatial scan statistic for detecting the most severe cluster of a disease

This paper focuses on the problem of detecting the geographical cluster with the most severe status in multiple groups of population given limited medical resources.Populations are grouped based on characteristics such as age,gender,and race.In the early stages of a disease,an outbreak may only present in specific population groups.Therefore,to efficiently detect the outbreak,we are particularly interested in monitoring and evaluating such groups.We define the objective of detection as the most severe cluster(MSC).Taking into account the interactions between population groups,a multivariate normal scan statistic is proposed to simultaneously determine the location and size of a significant MSC,as well as the specific population groups in which the MSC is located.The proposed method is applied to an example of lung cancer in New York State,where the MSC with the highest mortality rate at the aggregate level is detected.Further,the detection capacity of this method is evaluated using a simulation study based on the lung cancer example.

Dynamic multiple criteria group decision-making method based on intuitionistic fuzzy information

In the decision-making process,the decision information provided by decision makers over alter-natives may take the form of intuitionistic fuzzy numbers and come from different periods.The weight of information on decision makers,criteria,periods is usually completely unknown.To this issue,we first utilise hesitation degree information and introduce the concept of confi-dence degree function to determine the decision maker’s weights.Then we aggregate individual evaluation information into group evaluation information through intuitionistic fuzzy number weighted arithmetic averaging operator.We construct a nonlinear optimisation model to gain the criterion weights and apply the aggregate operator to gain the integrated rating value of alternatives in different periods,calculating the deviations of the integrated rating values with respect to their average.Then the period weights are been obtained by using the entropy method.According to the closeness coefficient between alternatives and ideal solution to sort the alternatives and select the optimal one.