| In 1965 American cyberneticist professor L.A. Zadeh published the paper named Fuzzy Sets, which announced the birth of fuzzy math. The theory of fuzzy sets extended the research field of mathematical theory and application from precise issues to fuzzy phenomenon. This theory covered the shortage of classical and statistical mathematics to some extent because of the concision and efficiency on handling complicated problems especially the system human intervened, thus drawing people's great attention. The information human used is language information, which has the character of fuzzy when described and the object described do not have the definite boundary. People made use of the fuzzy language to analyze, communicate, reasoning,judge and make decision in the field subjective factors worked, such as humanities and social science. Fuzzy theory obtained wide application in these fields. However, the most successful application field occurred in the field of automatic control and then formed the technology of fuzzy logic control, whose theoretical cores were just the fuzzy reasoning algorithm and technology.Since L.A. Zadeh proposed the compositional rule of inference (CRI) algorithm which based the Fuzzy Modus Ponens (FMP), the fuzzy control technology based on fuzzy reasoning widely applied in the field of industrial control and acquired significant economic benefit. However, CRI algorithm was doubted by many experts and scholars in its own field for the lack of strict logic basis. Based on this, Chinese scholar Wang GuoJun proposed the full implication triple I method of fuzzy logic and improved the CRI algorithms effectively.Introducing the fuzzy sets theory into complex problem decision-making is an important idea of decision model. The fuzzy sets theory is developing and improving constantly. Intuitionistic fuzzy sets and interval–valued intuitionistic fuzzy sets birthed successively after fuzzy sets and attracted people's increasing attention. Therefore, it is natural that introducing the interval–valued intuitionistic fuzzy sets (IVIFS) into complex problem decision-making. Because of the influence of the complex objective environment, the decision maker's professional skills, time and other factors, the decision maker cannot supply the precise preference information of decision scheme and a certain intuitionistic fuzzy interval is existed. At this time, using interval–valued intuitionistic fuzzy sets to describe the preference information of decision maker will be more comprehensive and careful and reflect the essential characteristics of the problem.The main study contents of this thesis are as follows:1) Introduce the concept of cut set of IVIFS, discuss its related properties and present the decomposition theory of IVIFS.2) Analyze the ambiguity of IVIFS essentially and make axiomatic definition of fuzzy entropy which accords with people's intuition.3) Define the residual implication of interval-valued intuitionistic fuzzy triangle norm about the interval-valued intuitionistic fuzzy reasoning. Derive the relationship between residual implication of interval-valued intuitionistic fuzzy triangle norm and that of triangle norm, and give the other basic properties of triangle norm.4) About the CRI and triple I algorithms of interval-valued intuitionistic fuzzy reasoning, discuss the general expression of the solution of the CRI and triple I algorithms on the MP and MT model of interval–valued intuitionistic fuzzy reasoning in a creative way, which is based on the interval–valued intuitionistic implication and triangle norm.5) Propose the multiple-target attribute decision method based on the inclusion degree of IVIFS for the use of interval–valued intuitionistic fuzzy in complex problem decision-making. |
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