Research On Group Decision Making Method Under Fuzzy Linguistic Preference Represented By 2-tuple Linguistic Representation Model

With the development of science and technology, and with the rapid increasing of knowledge and information, the decision-making problem becomes more and more complicate, a decision-maker can not resolve it because of his/her limited experience and wisdom. The decision-maker need consult with other decision-makers to seek more knowledge and information to deal with the complicated situations. Group decision-making basically solicits opinions from experts and combines these judgments into a coherent group decision.Group decision making is still the hot research issues in psychology and management research field that attracts scholars to study, because there are some contradictories in group decision-making, such as contradiction between individual rationality and group rationality, comparison between individual performance functions, the dilemma between effectiveness and unbiased regulation in conflicting group decision-making. There are still some questions in group decision-making need further theory study and case study.Meanwhile, it is difficult for decision-makers to express their intuitionistic preferences using accurate numbers, it is easier for decision-maker to use fuzzy numbers to express. And the decision-makers can express their preferences more accurately with the fuzzy linguistic preferences. All in all, due to uncertainty information, the understanding problem and the limited knowledge of decision-makers, there exists fuzziness in decision-making.There are many representation approaches for fuzzy linguistic preference, for example, interval-valued fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, linguistic label and 2-tuple linguistic representation model. Fuzzy group decision-making using different fuzzy linguistic preference representation method and aggregating method gets different decision results. There is not a perfect system for fuzzy group decision-making.Therefore, "Research on Group Decision Making Method under Fuzzy Linguistic Preference represented by 2-tuple Linguistic Representation model" was selected as the title of the dissertation. Researches on fuzzy group decision-making method were in progress to further study. The study will improve the effectiveness and rationality of fuzzy group decision-making, and will enrich the group decision-making theory and expand the method database for group decision-making. And the 2-tuple linguistic representation group decision-making system based on the theory research will simplify the application fuzzy group decision-making.The paper mainly studied the following problems such as the representation method of fuzzy linguistic preference, the consistency of fuzzy judgment matrix, the decision-making method under incomplete information, and the group decision-making method. The research mainly focused on the following four points.(1) Based on the criteria such as representation accuracy, information loss in processing, and operating research, different kinds of fuzzy representation methods and the confusion methods for different fuzzy linguistic preference representation were studied. And the suitable fuzzy linguistic preference representation method was selected, which set the foundation of the paper.(2) The study on judging the accuracy of a fuzzy judgment matrix was undergone to improve the effectiveness of the decision-making. The paper investigated the judgment of ordinal consistency of a fuzzy judgment matrix and the revising approach for a fuzzy judgment matrix without ordinal consistency. It also researched the threshold of consistency index according to different matrix cardinality to reveal whether the threshold was the same regardless of matrix cardinality.(3) Researches on decision-making under incomplete linguistic 2-tuple judgment matrix were carried out to enrich the method database for incomplete decision-making. When a decision-maker is not confident about some judgment or do not want to express their opinions, the decision-maker will give an incomplete fuzzy judgment matrix to show their preference.(4) Key points of group decision-making such as decision power designating, the process of group thinking, and the measurement of consensus were analyzed. The decision power designating method and aggregating approaches were investigated for group decision-making using 2-tuple linguistic representation model to improve the rationality of fuzzy group decision-making.Methods such as literature analysis, analytic hierarchy process, computer simulation, statistical analysis, analogous analysis, entropy method, questionnaire investigation, case study, object-oriented programming method and so on, were used in the research of the paper. Quantitative method and qualitative method was combined to deal with the study. And theories were applied to practical applications in the research.After designing the study plan for the research content, the research was deeply carried out with the aid of the above method. The main new ideas of the paper are as follows:(1) Based on the literature analysis on ordinal consistency and transitiveness theory of a binary relation, the paper proposed a new method to judge the ordinal consistency of a fuzzy judgment matrix. And a revising method was put forward, which was based on the concepts of non-transitive router number and non-transitive router contributing number. The new method will enrich the method database for ordinal consistency judgment and revising, and help the expert to improve his/her revising effectiveness.(2) The paper simulated 10000 3×3, 4×4, 5×5, 6×6 ordinal consistent fuzzy judgment matrices. The average and the standard deviation of its consistency index were calculated. The conclusion was that the threshold of consistency index should be different with different confidence degree and matrix cardinality, which solved the judging problem for consistency of fuzzy judgment matrix.(3) The properties of linguistic 2-tuple judgment matrix with additive consistency were studied based on the analysis of properties of fuzzy complementary judgment matrix and 2-tuple linguistic judgment matrix. The transitivity property of additive consistency was used to compute the indirect valued of an element. An estimating method was put forward to estimate the missing values in an incomplete linguistic 2-tuple judgment matrix, which provided a new solution for incomplete decision-making.(4) A new method was used to designate the decision power of each decision maker under group decision-making using linguistic 2-tuple representation. The basic idea of the decision power designating was that the consistency of each element was not the same, thus the decision power of the decision-maker should not be given the same priority. The responding individual aggregating method, the measurement for contribution degree of the decision-makers and consensus were proposed. And the group decision-making support system under 2-tuple linguistic representation model was designed based on the researched theory.In acquiring the performance framework for small and medium entrepreneur board listed companies, linguistic 2-tuple representation model was used to analyze the questionnaire about satisfied degree of the evaluation attributes and the linguistic 2-tuple matrices which were given by experts from different company. Thus the performance evaluation framework was build for small and medium entrepreneur board listed company.The application of the theory indicated that the 2-tuple linguistic representation model was suitable for representing fuzzy linguistic preference. Meanwhile, during the building of company performance evaluation indicators, the group decision-making system based on 2-tuple linguistic representation model was used to manipulate the evaluation given by experts for non-financial indicators. The input of the system is simple and the processing result is reliable. The system has the initialization modular, which will expand the application range.