Study On Method For Group Multi-attribute Decision-making Based On Triangular Fuzzy Number

In a democratic, just, harmonious society, the great decision-making should try one's best to meet the hopes and demands of the masses that are influenced by it. The masses reflect one's own hopes and demands through representatives, meanwhile, the representatives make up various kinds of committees, synthesize the masses' hopes and demands, meeting the wishes of masses and demands maximized. Moreover, in daily life, the daily decision-making which people meet every day, though the category not belonging to group decision-making, will solicit the suggestions of relatives and friends or the colleague in essence, then make the decision.Group multi-attribute decision-making (GMADM) is a kind of common decision-making problem, and an important branch in the field of decision-making analysis, which deals with the group decision-making problem with finite set of alternatives and multiple attributes. So far, many methods for solving GMADM Problem have been developed. But most of these approaches require exact information, which are pre-given by decision-maker, about values of decision-making parameters such as attribute weights, marginal utilities and state probability. Although different procedures have been proposed for the evaluation of parameters, it is often difficult to obtain their exact values. Usually, we call such group decision-making problem as group multi-attribute decision-making with incomplete information. Due to the complexity of objective things, the inaccuracy of decision-making information and the ambiguity of human thinking, the values of attribute to group multi-attribute decision-making are sometimes given the form of triangular fuzzy numbers, and the research of group multi-attribute decision-making problem for the values of attribute is triangular fuzzy numbers has attracted attention. It is studied and discussed in this dissertation.(1) For the triangular fuzzy number multiple attributive group decision-making problems, a new method for triangular fuzzy number group multi-attribute decision-making based on Ideal Solution which the attribute weights and the attribute values are both in the form of triangular fuzzy numbers is proposed. At first, the method presents definition and calculation of triangular fuzzy numbers, while defines the distance and similarity degree of triangular fuzzy numbers. Second, supposing the alternative's evaluation values under subjective evaluation attribute are triangular fuzzy numbers which are to express the vagueness and uncertainty of expert's evaluation values, the paper introduces experts' weight ideal which relies on evaluation attribute and the similarity degree of the expert's individual opinion, to reflect the expert's individual comprehensive important degree in the different evaluation attributives, and expert's individual opinion are assembly to gain triangular fuzzy number decision matrix of the group of experts on the alternative set. Finally, the ideal scheme for triangular fuzzy numbers and the proximity degrees are defined. A method based on Ideal Solution to triangular fuzzy numbers group multi-attribute decision-making problem is presented.(2) To solve the triangular fuzzy number multiple attributive group decision-making problems, the paper has proposed other new method for triangular fuzzy number group multi-attribute decision-making based on Group's Ideal Solution that the attribute values are in the form of triangular fuzzy numbers. At first, the method supposes the alternative's evaluation values under subject evaluation attribute are triangular fuzzy numbers which are to express the vagueness and uncertainty of expert's evaluation values, and introduces experts' weight ideal which relies on evaluation attribute and the similarity degree of the expert's individual judgments, to reflect the expert's individual comprehensive important degree in the different evaluation attributives; Second, the expert's individual judgments for each single evaluation attribute are aggregated into expert's group judgment by using the ideal point method, and a group's judgment decision-making matrix about the alternative set is obtained; At last, the positive and negative group's ideal schemes of triangular fuzzy numbers are defined. And an algorithm based on Group's Ideal Solution to triangular fuzzy numbers group multi-attribute decision-making problems is presented.