The Operation Laws Of Intuitionistic Fuzzy Values And Some Studies On Relevant Decision Models

Classic set theory is much mature and complete now. It is useful and widely used in relevant field and has become basis and foundation in modern mathematics. However, with the rapid development of scientific theory and technology, people have been aware of the limit and boundedness of classic set theory and found that it was not suitable for the situation where uncertainty and vagueness exist. Fuzzy set theory was proposed by Zadeh in1965, which can simulate the brain’s function in handling fuzzy information. As soon as fuzzy set theory arose, it has been studied and disscussed frequently because it’s very simple and convenient to utilize fuzzy set to solve fuzzy problems. Fuzzy set is the generalition of classic set and has the analogous operations and properties with it. Later, intuitionistic fuzzy set,which is the generation of fuzzy set,is put forward by K. Atanassov in80s in the previous century. Recently,intuitionistic fuzzy set has also arosed much attention and investigation.In chapter1,we introduce the basic idea and struct of this paper and elaborate the basic concepts of this paper with the popurse of providing visual understanding and comprehension before main body parts.Fuzzy set theory is introduced in chapter2,and it’s primary operations and operational rules are also presented in this part. Then,we mainly study fuzzy preference relations which is one of the applications of fuzzy set theory. We generalize the concept of consistency of fuzzy preference relations, by which some optimization models are established to solve some kinds of decision making problems.Intuitionistic fuzzy set theory is brought forth in chapter3,which is extended from fuzzy set theory. Intuitionistic fuzzy set has the identical operations and operatinal rules with classic set and fuzzy set,and they are also showed in this part. The four species of intuitionistic fuzzy set are researched particularly in the last of this part,where subtraction and division are added at the existing addition and multiplication. The relationships between the four species of intuitionistic fuzzy set are investigated necessarily to ensure the associativity and wholeness of the four species.In chapter4,the concept of intuitionistic fuzzy value is illustrated and the corresponding operations and operational rules are also given in this part. Intuitionistic fuzzy value has some important attribute values for comparing or ordering.like score and accuracy. We introduce a new attribute value called controversy for intuitionistic fuzzy value, by which som new notations and a new utility are provided in the following parts. A new ordering method can be natually applied in intuitionistic fuzzy values.In chapter5,this paper attempt to generalize the concept of fuzzy set and put forward the concept of generalized fuzzy set. At last.the corresponding concepts of generalized fuzzy set derived from intuitionistic fuzzy set are presented.which are score,controversy and accuracy.