Research On Intuitionistic Fuzzy Implication And Fuzzy Multiple Attribute Decision Making Problem

In recent decades, with the rapid development of fuzzy theories, a great deal of research achievements have been applied in control system and decision making, which makes fuzzy control and fuzzy decision making gets rapid developments. With the application of fuzzy theory in control theory, the control system can be established by extracting rules from knowledge and experience of control process, which can avoid the dependence on precise mathematical models in classical control theory. With the application of fuzzy theory in decision making, the problems of uncertain information, which cannot be solved in classical decision theory, have been processed effectively. Based on fuzzy theories, the uncertain events and properties can be view as fuzzy sets and processed utilizing membership functions. Fruitful achievements have been obtained, but the fuzzy theory still need to be improved in many aspects. The choosing principles of implication operators in fuzzy control system have rarely been studied. And the research related to the ranking problems of index sets and the expressing problems of uncertainty weights need to be deepened. In view of above problems, based on the cut sets of intuitionistic fuzzy sets, the studies on fuzzy control and fuzzy decision making are presented in this thesis, and there are four parts included in the dissertation:1. For the establishment of intuitionistic implication operators, two methods are proposed utilizing the intuitionistic fuzzy cut sets:In the first method, cut sets and representation theorem of intuitionistic fuzzy sets are utilized, through triple valued fuzzy implications as well as fuzzy relations to obtain seven intuitionistic fuzzy implication operators. In the second method, the Lebesgue measure of the fuzzy implications with value one and zero is used, and one intuitionistic fuzzy implication operator can be got. Finally, properties of those operators are discussed. The research results will provide a new scheme for the selection of implication operators in fuzzy controller, and provide theoretical and technical support for the construction of fuzzy system.2. A new method for ranking fuzzy numbers is presented, which is named as possibility-based comparison relation. The method is based on cut sets and comparison relation of interval values. Three parts are involved in the section. Firstly, a new formula of cut sets of interval values is introduced. Then, with the help of the formula, a new comparison relation on interval values is presented, and applied to the issue of ranking fuzzy numbers using fuzzy attitude functions. Secondly, some numerical examples are used not only to demonstrate the procedure of the proposed method but also to compare with previous methods. Finally, by means of the ranking method, a fuzzy attitude-based decision model is introduced to solve fuzzy decision making problems. Some examples are given for illustration. The achievements in the presented work will provide an effective ranking method with good results for decision making problems.3. To solve the uncertainty of the index set weight in fuzzy multi-attribute decision problem, the value of weight has been extended from real number to interval number and intuitionistic number, a series of new concepts including interval entropy, intuitionistic entropy, interval similarity measure, intuitionistic similarity measure, interval distance measure, and interval inclusion measure of fuzzy sets are introduced. Meanwhile, some theorems and corollaries are proposed to show how these definitions can be deduced from each other. And then, based on interval entropy, a fuzzy multiple attribute decision making model is set up. In this model, interval entropy is used as the weight, by which the evaluation values of all alternatives can be obtained. Then all alternatives with respect to each criterion can be ranked as the order of the evaluation values. At last, a practical example is given to illustrate an application of the developed model and a comparative analysis is made.4. In the sixth chapter, how to measure the information content of the fuzzy relation with uncertainty is studied. The interval information content of the fuzzy relation is defined, and some general information content measures of fuzzy relations are present here. With the help of the interval information content, the optimization of fuzzy implication operators can be realized. The combination of the interval information content and the possibility-based interval value comparison relation can be used to rank the fuzzy implication operators. Using the similarity measure of interval value, the implication operators can be clustered. The clustered results show that normal and abnormal implication operators can be differentiated. Finally, based on the optimal clustering results, the attribution of any implication operator can determined. Research results will provide new methods for the selection of implication operators in control system.