A Method Exploration For Transforming Interval-valued Vague Set Into Fuzzy Set And Application

In the real word, there exists quite a lot of information that is uncertain, ambiguous and incomplete. How to describe the information accurately is the most important problem in the science research. There are only two kinds of relations between the elements of the cantor set and the cantor set including belonging or not belonging to. But when the concept of the set itself is ambiguous, some elements cannot be simply regarded as belonging to the set. Thus, the United States of American C y b emetics Professor L.A Z a de h popularized the concept of cantor set in1965and fuzzy set theory is put forward.Because vague set can only express the support and opposition, cannot express indeterminacy (hesitation) clearly. A lot of fuzzy information is unable to be represented and treated with Fuzzy set theory. Thus, another concept-vague set theory to deal with fuzzy information is proposed by W. L. G au and D.J.B u e h r e r, Tai Wan scholars. Later, Vague Set is able to handle a lot of information that is much more uncertain and fuzzy, which is regarded as a development of Fuzzy set. It promote the research process of fuzzy information as the Vague Sets is proposed and is also a new and more powerful tool for processing information and decision-making. But, it is very short since V ague set theory has been proposed so far, and its basic theory is not perfect. Moreover it is necessary to transform Vague Set into Fuzzy sets on the basis of the existing literatures, so by means of more research matures of Fuzzy Sets to solve the unsolved problem only by Vague Sets.However, some fuzzy information is not more and more obvious when dealing with the practical problems. There is an object to research the degree of support and opposition with the Vague Set theory launched and exchanged from a single real value into interval valued. So the paper presents a novel concept-Vague Set. Vague Sets knowledge degree is defined in the paper to resolve the Vague Sets multiple attribute decision-making, consolidating the existing literature. That real type group making-decision sore function is extended to the interval value Vague Sets. The method based on theory of vague set and some methods for transforming Vague set into Fuzzy set are investigated, which is about interval-valued Vague set is transformed into Fuzzy set. Based on some aggregation operators, including interval-valued Vague set weighted arithmetic aggregation operator and interval-valued Vague set weighted geometric aggregation operator, belongingness degree is defined. Furthermore, a effective sorted method to interval-valued Vague sets are given, and its validity is explained by analyzing a practical examples.