APPROACH FOR FUZZY MULTI-ATTRIBUTE DECISION-MAKING WITH FUZZY COMPLEMENTARY PREFERENCE RELATION ON ALTERNATIVES

In presented fuzzy multi-attribute decision-making （FMADM） problems, the information about attribute weights is interval numbers and the decision maker （DM） has fuzzy complementary preference relation on alternatives. Firstly, the decision-making information based on the subjective preference information in the form of the fuzzy complementary judgment matrix is uniform by using a translation function. Then an objective programming model is established. Attribute weights are obtained by solving the model, thus the fuzzy overall values of alternatives are derived by using the additive weighting method. Secondly, the ranking approach of alternatives is proposed based on the degree of similarity between the fuzzy positive ideal solution of alternatives （FPISA） and the fuzzy overall values. The method can sufficiently utilize the objective information of alternatives and meet the subjective requirements of the DM as much as possible. It is easy to be operated and implemented on a computer. Finally, the proposed method is applied to the project evaluation in the venture investment.

Two-phase TOPSIS of uncertain multi-attribute group decision-making

To solve the uncertain multi-attribute group decision-making of unknown attribute weights,three optimal models are built to decide the corresponding ideal solution weights,standard deviation weights and mean deviation weights.The comprehensive attribute weights are gotten through the product of the above three kinds of weights.And each decision maker＇s weighted decision matrices are also received by using the integrated attribute weights.The closeness degrees are also gotten by use of technique for order preference by similarity to ideal solution（TOPSIS） through dealing with the weighted decision matrices.At the same time the group decision matrix and weighted group decision matrix are gotten by using each decision-maker＇s closeness degree to every project.Then the vertical TOPSIS method is used to calculate the closeness degree of each project.So these projects can be ranked according to their values of the closeness degree.The process of the method is also given step by step.Finally,a numerical example demonstrates the feasibility and effectiveness of the approach.

Method for Risky Multiobjective Group Decision-Making and Its Application

The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.

Dynamic hesitant fuzzy linguistic group decision-making from a reliability perspective

A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.

生产中的模糊贝叶斯决策模型

生产中的模糊贝叶斯决策模型李容华（湖南财经学院）一、问题的提出在统计决策中，人们通常用先验概率作决策．这种决策是根据历史资料过经验判断而得到的．实践证明，这种决策难以准确地反映生产现实，具有局际性．我们如果能在其决策中补充现实中发生的新信息，新资料，...

AGGREGATION OF FUZZY OPINIONS UNDER GROUP DECISION-MAKING BASED ON SIMILARITY AND DISTANCE

In this article, a new method for aggregating fuzzy individual opinions into a group consensus opinion is proposed. To obtain the aggregation weights of each individual opinion, a consistency index of each expert with the other experts is introduced based on similarity and distance. The importance of each expert is also taken into consideration in the process of aggregation. Finally, a numerical example is presented to illustrate the efficiency of the procedure.

An Approach to Resolving Two Paradoxes in Probability Theory

A new mathematical expectation formula with some hypotheses, notions and propositions was given to get rid of the challenge of St. Petersburg paradox and Pascal's wager. Relevant results show that it is very effective to apply the model to solve the expected revenue problems containing random events with low proba-bility but high revenue. This work also provides the probability theory with a more widely applied perspective in group decision-making.