Multiple Periods Fuzzy Multiple Criteria Decision Making Methods

Multiple criteria decision making(MCDM) is an important part of decision theory. It is a decision making method which refers to the limited alternative with the multiple attributes. The method is used to evaluate and sort the alternative or select the best alternative according to some decision rules. The limitation of the traditional MCDM is that its research is in a clear environment. However, uncertainty and fuzziness are universally found in the real decision-making process. In the modern decision analysis, some decision problems usually involve in imprecise, uncertain and subjective data, which could cause the decision process more complex and challengeable. Moreover, each decision maker has limited knowledge, different preference structures and complex decision making background, and some attributes are more abstract. In reality, most of decision makers are usually willing to give the linguistic variables or fuzzy variables to reflect the attribute information, rather than crisp values. At the same time, the decision making process could be formulated by many decision makers or happened in multiple periods, and the multiple periods’ information of the experts or decision makers need to gather. Hence, in the fuzzy environment, it is a key problem to obtain the final results of the decision making with the reasonable, the accurate and effective methods based on the fuzzy set theory, MCDM method, aggregation theory and optimization theory.Therefore, some fuzzy multiple criteria decision making(FMCDM) methods are proposed to effectively express the fuzzy preference informations based on the fuzzy set theory, MCDM method, and aggregation operator theory. In the FMCDM, the weights of attributes play a significant role since they directly affect the accuracy of the decision making and the ranking results of the alternatives. In order to meet decision maker’s true intentions and grasp the rules and the determining factors of fuzzy informations, we efficiently determine the weights of attributes in the fuzzy decision making process. At the same time, the time is considered in the paper and some combination weight methods have been proposed to determine the time weight. The dynamic fuzzy multiple criteria decision making(DFMCDM) methods are also proposed based on the time weights. The contents and the related results are specifically given as follows:(1) The attribute weights affect the decision making results. In FMCDM, in order to determine the partial information related attribute weight, a linear programming model is proposed based on the maximizing deviation degree. A MCDM method with generalized fuzzy numbers(GFNs) is also proposed to meet the decision maker’s preference. Moreover, Hausdorff distance is given to determine the distance between the GFNs. The distance can not only reduce the computational complexity, but also improve the robustness of the assessment result. In the fuzzy decision making process, because the decision making results are still fuzzy numbers, a ranking formula with a modified possibility degree is adopted to rank alternatives. Finally, a numerical example is introduced to illustrate the proposed method. The experimental results indicate that the method could adjust the parameters of GFNs to meet the different assessment requirements of the decision makers which could help to improve the accuracy of decision results.(2) In FMCDM, in order to reasonably, accurately and scientifically make decision, we not only comprehensively consider the influence of the attribute weights, but also make full use of the fuzzy informations contained in the attributes. Therefore, a DFMCDM method is proposed. This method not only considers the combinational weight of the decision makers with the objective and subjective preference, but also considers the effect of time weight. In the proposed method, according to the advantages and disadvantages of subjective weight and objective weight, a mathematical programming model is used to determine the combinational weight. A basic unit-interval monotonic(BUM) function based approach is used to calculate the time weight in the multiple periods’ decision making process. In addition, a distance measure of membership function is introduced to effectively measure the degree of difference between the alternatives and fuzzy positive ideal solution or fuzzy negative ideal solution in the fuzzy Technique for Order Preference by Similarity to Ideal Solution(FTOPSIS), which make the final evaluation results more reasonable and accurate.(3) Information aggregation is an important research object of decision theory. The dynamic power weighted average(DPWA) operator is proposed based on the aggregation operator and time weight. Then the dynamic comprehensive evaluation method(DCEM) is also proposed based on the DPWA operator. And then the DCEM is extended to fuzzy environment, in order to consider the uncertainty information, decision information distribution of multi stages as well as the traditional weighted average operator without considering the integration among the data relationship, a dynamic multiple criteria decision making method with uncertain power geometric weighted average operators is proposed. In the method, combining the fuzzy set theory, the uncertainty information in multi stages are aggregated, and the support degree among the data relationship are also considered. The ranking method based on possibility degree is used to select the optimal alternative. Moreover, the processes of handling fuzzy evaluation information are strengthened, and the evaluated results are more close to the reality.In a word, the combinational methods of the fuzzy set theory, MCDM methods and aggregation theory have the certain universality. These methods are not only applied in supplier selection, performance evaluation, optimal investment etc., but also provide the certain reference for the finance, information, military science, medical science and other fields.