Research On Multiple Attribute Decision Making Under Linguistic Environment

Multiple attribute decision making (MADM) is an important part of modern decision-making theory, and has a broad application in the field of modern politics, economy, medical science, military, science and technol-ogy, etc. In the process of dealing with actual making decision problems, due to the fuzziness of human thinking, differences in knowledge and data, the complexity and uncertainty of the actual decision making problems, some attribute information of the decision problems is vague and difficult to use ac-curate quantitative form to describe, but to use "good", "general", "poor" and other natural language form to express the will of the people. Therefore, the research on multi-attribute decision making method of linguistic information is particularly important.So far, the main methods used to aggregate language information are the following:extension principle method, symbolic method,2-tuple repre-sentation method and direct operation method, etc. For the extension princi-ple method and symbolic method, the aggregated results are often not fully matched to the linguistic terms in the initial linguistic terms, and be processed by an approximate method, in this process, it is easy to produce informa-tion loss. The 2-tuple representation method transforms linguistic informa-tion into 2-tuples, the operation rules on the two tuple are defined, and the corresponding aggregation operators are proposed. But this method is only suitable for linguistic variables with equidistant labels and has its own lim-itations. For the fourth method, the aggregation result in some cases may not match any of the initial term sets and may cause a counterintuitive phe-nomenon. In addition, the product form of real number and linguistic variable has no meaning in practical problems, and is hard to resolve.In order to solve the problems existing in the process of dealing with lan-guage information, this paper generalizes the concept of fuzzy multiple sets to linguistic environment, and proposes a new fuzzy linguistic multiple set to deal with linguistic information. Therefore, the main work on the following aspects:1. The fuzzy multiple sets be extended to linguistic environment, put for-ward the concept of fuzzy linguistic multiple set, then define order relation in fuzzy linguistic multiple set and give a conversion relationship between linguistic term set and fuzzy linguistic multiple set. Two kinds of new dis-tance measure for fuzzy linguistic multiple set are proposed, that is, additive distance measure and multiplicative distance measure.2. Based on the additive distance measure function, we propose a new aggregation model of language information. By solving the model, a new lan-guage information aggregation operator FLMWAA is derived, and some de-sirable properties of the FLMWAA operator are studied. Then, a new method for linguistic multiple attribute decision making based on the FLMWAA op-erator is given. An example is given to illustrate the feasibility and validity of the new approach to multiple attribute decision making application.3. Based on the multiplicative distance measure function, we propose a new aggregation model of language information. By solving the model, a new language information aggregation operator FLMWGA is derived, and some desirable properties of the FLMW GA operator are studied. Then, a new method for linguistic multiple attribute decision making based on the FLMWGA operator is given. An example is given to illustrate the feasibil-ity and validity of the new approach to multiple attribute decision making application.