| Multi-attribute decision making is an important research direction of management science and engineering, as well as an important branch of modern decision science. Its theory and method, no matter in theory or in practice, have a promising prospect in economics, management, engineering, and military and other fields. With a large number of nonlinear problems emerging in economics, management science, biology, and systems engineering, besides the complexity and uncertainty themselves and the ambiguity of human thinking, the studies of nonlinear problems and fuzzy multi-attribute problems draw most attention of the whole decision analysis academic circles. The fixed point theory of nonlinear operators is applied widely in equilibrium problems of economic management fields as an important tool of the modern management science and economics theoretical research. Therefore, to study the fixed point theory of nonlinear operator and fuzzy multi-attribute decision problems are of essential theoretical meaning and high applicable value. Thus, the purpose of this thesis is to study common fixed point theorem of multiple mappings in several kinds of generalized metric spaces and the multi-attribute decision making problem under uncertain condition, mainly include as follows:In chapter one, the research background, purpose and significance are expounded. The research status of fixed point theory of nonlinear operators and fuzzy multi-attribute decision problems are described for a more comprehensive overview, and the main contents of this thesis are summarized.In chapter two, the common fixed point theorems of self-mapping sequence, four non-self mappings, and any even number of non-self mapping in complete cone metric space are discussed in different contractive condition, and some illustrate examples are furnished as these results'inportant support and application. These results generalize series of important theorems in metric space (include cone metric space) and provide theoretical basis to solve equilibrium problems of the more general economic management.In chapter three, firstly the concepts of intuitionistic fuzzy (g,(?))—contraction for single-valued mapping and multi-valued mapping are established, with the corresponding fixed point theorems are followed in intuitionistic fuzzy metric spaces. Secondly, two common fixed point theorems under some contraction for any even number of compatible mappings in complete intuitionistic fuzzy metric spaces are obtained. As an application of the main results, a common fixed point theorem for four finite families of mappings in complete intuitionistic fuzzy metric spaces is proved. These results generalize the main conclusions draw by relevant references in many aspects and provide a new theoretical basis to solve equilibrium problems of economic management under fuzzy environment.In chapter four, the concepts of E.A. property and common E.A. property in L-fuzzy metric spaces are established, with the corresponding common fixed point theorems for two pairs of mappings in L-fuzzy metric spaces by using common E.A. property are followed. Then two common fixed point theorems under some contraction for any even number of compatible mappings in complete in L-fuzzy metric spaces are obtained. These results generalize the main conclusions draw by relevant references in many aspects and provide a new theoretical basis to solve equilibrium problems of economic management under uncertainty environment.In chapter five, in considering the uncertainty of attribute values, it is also considered the uncertainty of the environment. With the idea of probability theory, the probability ordered weight average (P-OWA) operator and probability ordered weight geometric averaging (P-OWG) operator are proposed firstly, their basic characteristics are investigated. The multi-attribute decision making approaches based on these two operators are developed and an illustrative example is given. In what follows, the weighted continuous ordered weighted geometric averaging (WC-OWG) operator is extended, the probabilistic weighted continuous ordered weighted geometric averaging (PWC-OWG) operator, probabilistic ordered weighted continuous ordered weighted geometric averaging (POWC-OWG) operator and probabilistic combined continuous ordered weighted geometric averaging (PCC-OWG) operator are proposed and their basic properties are studied. Also, an uncertain multi-attribute single person decision making method based on PWC-OWG operator and an uncertain multi-attribute group decision making method based on PCC-OWG operator are developed and an illustrative example is given. These studies extend the multi-attribute attribute decision-making theory, while these operators in many other fields, such as investment decisions, location, market research, choice of health care regimens also have a good prospect.In chapter six, study on the multi-attribute decision making problems with attribute values are intuitionistic fuzzy number and interval-valued intuitionistic fuzzy number. The induced generalized intuitionistic fuzzy ordered weight average (UI-GIFOWA) operators and induced generalized interval-valued intuitionistic fuzzy ordered weight average (UI-GIIFOWA) operators under uncertain environments are proposed. An approach to multi-attribute group decision making with fuzzy linguistic information is developed based on the UI-GIFOWA and the UI-GIIFOWA operators. These methods are then applied to solve some actual problems in the fields of venture capital.In chapter seven, using retrospective survey methods,3 three A-level comprehensive hospitals were researched in Jiangxi province and 1440 hospitalized cases due to non-small cell lung cancer (NSCLC) were collected. The choice of chemotherapy regimen of NSCLC is discussed by the approach to multi-attribute decision making based on UI-GIFOWA operators. The optimal chemotherapy regimen of NSCLC is obtained.In chapter eight, sums up the main content and the main conclusions in the entire thesis, and then puts forward the need for further refinement and in-depth research directions in the future.
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