A Study On Theories And Methodologies For Fuzzy Multi-objective Decision Makings With Their Applications

Decision-making is activities that human realize the world. Many decision-making problems are often fuzzy, multi-layer, multi-objective and multi-person. Based on the Engineering Fuzzy Sets Theory(EFST) established by Prof. Chen Shouyu, this paper mainly focuses on theories, models and methodologies for fuzzy, multi-layer, multi-objective and multi-person decision-making problems with their applications, and are of value to scientific researches and real applications. The results are as follows:Weight and qualitative objective are two types of primary preference information in fuzzy multi-objective decision-making. Based on the theory of unit system for non-structural decision-making proposed by Prof. Chen Shouyu, a new methodology and algorithm are proposed to resolve the objective weight and relative membership degree of qualitative objective using fuzzy value of relative important degree of adjacent objectives and alternatives. Based on pairwise comparison, the fuzzy optimum-seeking model, the set-value statistics theory and Borda method, several models and methods are proposed to aggregate individual preference into a group preference. These methods can effectively utilize individual preference, and make it easy to convert linguistic estimation into fuzzy value.According to the characteristics of optimum-seeking, pattern recognition and clustering with fuzzy information in real world, ordinary fuzzy number and ordinary fuzzy distance are introduced in the optimum-seeking model and the fuzzy pattern recognition model, and special fuzzy numbers and special fuzzy distance are introduced in fuzzy clustering model which were all proposed by Prof. Chen Shouyu. The research enriches the EFST, and makes it possible for these models to be applied more widely and effectively.Based on the concept of relative membership degree in the fuzzy sets theory, F-LINMAP model and F-TOPSIS model are proposed. Traditional Linear Programming Techniques for Multidimensional Analysis of Preference(LINMAP) decision-making model is improved to non-structural or semi-structural decision-making problems with special fuzzy numbers and special fuzzy distance, and traditional TOPSIS model is improved to fuzzy decision-making model with ordinary fuzzy numbers and ordinary fuzzy distance. It proved that the F-LINMAP and the F-TOPSIS are more easy, effective, useful and practicable than traditional models.Considered universality of group decision-making, the fuzzy optimum-seeking model is applied to group decision-making respectively according to the decision-making sequence ofintegration-autarchy or autarchy-integration. New decision-making models are proposed depending respectively on the combination of the fuzzy optimum-seeking model, Borda method, the F-LINMAP and the F-TOPSIS. In order to demonstrate the advantages of relative membership degree in optimum-seeking, pattern recognition and clustering, SWA decision-making method is be studied as an example. Based on the EFST, integrative fuzzy group decision-making model is established, and it can be applied to individual decision-making, group decision-making, fuzzy decision-making and traditional decision-making. All method and conception is presentd to deal with multi-layer fuzzy group decision-making problems with the optimum-seeking model.Applications of these new models and methods are mainly focused on four problems: the research on threat judgment model and method with the new optimum-seeking model and new fuzzy pattern recognition model, the analysis of groundwater resource with the new fuzzy clustering model, the research on water resources and macro-economic sustainable development of DaLian with the multi-layer multi-criteria multi-person fuzzy optimum-seeking method and Tchebycheff decision-making theory, and the analysis of operational effectiveness for warship with the multi-layer multi-criteria multi-person fuzzy optimum-seeking method.All models and methods presented in this paper are depended on the EFST. And at the same time they enrich the EFST theoretically and...