Study On Multiple Attribute Group Decision Making Under Linguistic Environment

Multiple attribute decision making (MADM) addresses the problem of choosing an optimum choice that has the highest degree of satisfaction from a set of alternatives that are characterized in terms of their attributes. It is a great branch of operational research and management science and information science. When we make decisions, it often involves uncertainty with objective nature or subjective nature. Uncertainty is represented by randomness, fuzziness and roughness. Multiple attribute decision making under uncertainty is an extension and development of classic precise numerical decision making methods. In this thesis, based on linguistic approach, some new approaches are put forward. We obtained the following results.Firstly, we propose a method for multi-attribute decision making problems with linguistic information, in which the preference values take the form of linguistic variables. An aggregating operator named linguistic weighted arithmetic averaging (LWAA) operator is introduced to aggregate the given decision information to get the overall preference value of each alternative. Based on the idea that the attribute with a larger deviation value among alternatives should be evaluated a larger weight, a method to determine the optimal weighting vector of LWAA operator is developed under the assumption that attribute weights are completely unknown. The proposed approach is extended to the situation where partially weight information can be obtained by solving a constrained non-linear optimization problem.Secondly, we discuss the MADM problems with preference on alternatives, in which the attribute values take the form of linguistic variables and the preference on alternatives is linguistic preference relation. We develop a model to determine the optimal weighting vector of attributes under the assumption that attribute weights are completely unknown. The model integrates the linguistic decision matrix and the linguistic preference relation as a whole. As symbolic approaches, the proposed methods are of great flexibility to deal with mixed MADM problems. We also investigate MADM problems with interval multiplicative preference relation on alternatives, in which the attribute values also take the form of interval values. At the end of this section, we point out what we should pay attention to when using the presented methods to solve practical problems.Thirdly, fuzzy comprehensive evaluation method is extended to linguistic situation to solve the case where elements in evaluation matrix take the form of linguistic variables. In the developed model, the LWAA operator is selected as the synthesis evaluation function. The overall performance level thus is obtained in terms of the maximum grade of membership rule. In group setting, the LWAA operator is again used to aggregate individual preference and the group collective evaluation matrix is got.Finally, group decision making problem based on incomplete multiplicative and complementary judgement matrices is discussed. The two kinds of linguistic judgement matrices are transformed to corresponding numerical judgement matrices at first place. Based on the consistency of multiplicative judgement matrix and addition consistency of complementary judgement matrix, a constrained optimization model is therefore constructed. Its explicit solution under some situation and the properties of the given solution are also discussed. The ranking of alternatives or selection of the most desirable alternatives can be directly obtained according to the presented method.Through out this thesis, we give some examples and applications to demonstrate and verify the proposed approach.