Multi-Criteria Decision Making Approaches With Uncertain Information Based On Trapezoidal Fuzzy Number And Their Application Study

Decision making plays an important role in people’s daily life, which is widely used in other areas. However, in many decision making context, because of the complexity of problem, the lack of knowledge, the limit of time pressure, the uncertainty of objectives, and in many cases, obtaining exact information is either impossible or very expensive, many multi-criteria decision making problems are often accompanied by a lot of uncertainty, therefore, to study the multi-criteria decision making theory and methods with uncertain information has important theoretical significance and practical value. This paper studied such problems with fuzzy information, proposed a variety of fuzzy multiple criteria decision making methods and established some relative mathematical models to solve real problems. Finally, though some empirical studies to demonstrate the feasibility and effectiveness of the proposed methods.(1) For the MCDM problems with trapezoidal fuzzy number establishing a hierarchical multi-objective linear programming model, and using lexicographic optimization methods to solve the weight number of evaluation projects and ideal project. Meanwhile, according to Hamming distance formula to solve the distances of alternatives from the ideal solution are calculated to determine their ranking order.(2) For the MCDM problems with intuition fuzzy number, where individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives are taken into accout to represent the interactive characteristics among the criteria or preference of decision makers, proposed a fuzzy multi-criteria decision making model based on intuition trapezoidal fuzzy number and Choquet integral. In this model, multi-criteria intuition trapezoidal fuzzy number is introduced to capture the DM’s preference information. Then, the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data. Further, Choquet integral-based Hamming distance between intuition trapezoidal fuzzy number is captured to aggregate attributes of decision maker and calculate the positive-ideal solution and negative-ideal solution, and using fuzzy TOPSIS to determine the relative closeness coeffcients of alternaives and the ranking order of all alternatives.(3) In order to further demonstrate the feasibility and practicability of the proposed model (hierarchical multi-objective linear programming model based on trapezoidal fuzzy number), we conducted an empirical research on a number of industry enterprises in five cities, and collected the data of economic benefit, resource saving, environmental level and social benefit to investigate the performance of these enterprises in the aspects of economy, resource, environment and contribution. By using the proposed model to obtain the ranking order of enterprises of different areas, and doing a comparative analysis to get the conclusion.(4) Using the fuzzy multi-criteria decision making model based on intuition trapezoidal fuzzy number and Choquet integral to evaluate venture investment projects. According to investigate five venture investment enterprises in an area, collected the data in the aspects of technical level, market size, product innovation, industry environmental and government support. The result shows the comprehensive rankings of these enterprises in the four aspects. According to the analysis, practicality and feasibility of our model will be evidenced and highlighted.