The Research Of Some Questions On Multi-valued Interval Intuitionistic Fuzzy Soft Sets

The objective world is full of fuzziness and incompleteness. The probability theory, rough set theory and fuzzy set theory describe the uncertainty from different angles, and they make great contribution to uncertain problem processing. But they have the problem of insufficient parameters. The soft set, as a new mathematical tool, deal with these uncertainties from the perspective of parameterized problem. The soft set has caught the attention of many scholars since it was proposed. Multi-valued intuitionistic fuzzy set implicates that different expert offer different evaluation results about one object, and the same expert get different judgement from different angles. But the multi-intuitionistic. fuzzy sets don’t consider the interval membership and the non-membership degree. In this thesis, on the basis of previous research, multi-valued intuitionistic fuzzy sets is generalized to multi-valued intuitionistic fuzzy soft sets, its properties and application in uncertain decision making, the work is as follows:(1) This thesis comprehensively analyses the soft set, fuzzy soft set, multi-valued intuitionistic fuzzy sets, the concept of multi-valued interval intuitionistic fuzzy sets will be put forward considering the interval number theory, after that, the concept of multi-valued interval intuitionistic fuzzy soft sets also be given combined with the soft sets, then the relevant operations(union, intersection, complement, subsets) and characters will be studied, therefore, it’s better to describe and solve the uncertain problems.(2) The multi-value interval intuitionistic fuzzy soft level set is proposed by introducing the level set to multi-valued interval intuitionistic fuzzy soft sets, then this thesis discusse and prove its related properties. Considering the requirements are different towards different properties and decision criterions, the concept of λ-leval set based on variable threshold is proposed, and some commonly used level cut sets is presented.(3) The multi-valued intuitionistic fuzzy soft sets is applied to multiple attribute decision making, and the corresponding decision algorithm is given. An axample is used to verify it is feasible and effective.