Eigenvector Method for Ranking Alternatives with Vague Value Measurements

An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on four assumptions for evaluating alternatives, a ranking eigenvector is defined. And then it is proved, based on positive matrix theory, that the EIM＇s eigenvector corresponding to the maximal eigenvalue is the ranking vector. For alternatives whose characteristics are presented by vague sets, the proposed techniques can evaluate the degree of suitability to which an alternative satisfies the decision-maker＇ s requirement efficiently.

Multi-attribute decision-making based on subjective and objective integrated eigenvector method

An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attributes and objective information is expressed by a decision matrix. An eigenvector method integrated the subjective fuzzy preference matrix and objective information is proposed. Two linear programming models based on subjective and objective information are introduced to assess the relative importance weights of attributes in an MADM problem. The simple additive weighting method is utilized to aggregate the decision information, and then all the alternatives are ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the method. The result shows that it is easier than other methods of integrating subjective and objective information.

Method for multiple attribute decision making based on incomplete linguistic judgment matrix

With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.

Model of interval multi-attribute optimization for overseas oil-gas projects

Because of the incompleteness and uncertainty in the information on overseas oil-gas projects, project evaluation needs models able to deal with such problems. A new model is, therefore, presented in this paper based on interval multi-attribute decision-making theory. Analysis was made on the important attributes （index） and the re- lationships affecting the basic factors to the project eco- nomic results were described. The interval numbers are used to describe the information on overseas oil and gas projects. On these bases, an improved TOPSIS model is introduced for the evaluation and ranking of overseas oil and gas projects. The practical application of the new model was carried out for an oil company in selecting some promising blocks from 13 oil and gas blocks in eight dif- ferent countries in the Middle East. Based on these inno- vative studies, some conclusions are given from theoretical and application aspects. The practical application shows that the introduction of interval numbers into the evaluation and ranking of the overseas oil and gas projects can lead to more reasonable decisions. The users can do the project evaluation based on the comprehensive values as well as based on some preferred index in the project evaluation and ranking.

Group Decision-Making Method of Entry Policy During a Pandemic

Omicron,the new mutant coronavirus,has spread rapidly globally,attracting close attention from different stakeholders worldwide.The complex and constantly changing epidemic situation has had a new impact on the world.Therefore,this paper focuses on the characteristics of the rapid spread of the COVID-19 variant strain.Generally,epidemic prevention experts conduct preliminary screening as part of the existing epidemic plan database according to the current local situation,after which they sort the alternatives deemed more suitable for the situation.Then the decision-makers identify the most divergent expert group,plan for consultation and adjustments,and finally obtain the plan with the smallest divergence.This article aims to integrate the experts'opinions with the method of minimizing the differences,which can maximize the expert consensus and help organize the schemes that best meet the epidemic situation.The experts'negotiation and iteration of the differences in the initial plan align with the current complex and dynamic epidemic situation and are of great significance to the rapid formulation of plans to achieve effective prevention and control.

Preference levels for clusters of alternatives

In the decision-making tasks for ranking the alternatives and choosing the best ones,procedures on the digraphs are often used.A digraph of the aggregated relation on a set of alternatives for information of experts or criteria is preconstructed.If the digraph does not contain any cycles,then the Demukron algorithm for partitioning the digraph into levels can be used to order the alternatives by preference.This algorithm cannot be applied if there are clusters consisting of equivalent alternatives.In the paper the algorithm for partitioning an arbitrary digraph of into preference levels is proposed.In contrast to the standard procedure,the digraph of the aggregated relation admits the presence of cycles,and,consequently,of equivalent vertexes-alternatives.The vertexes in any cycle of digraph belong to one level of preference.