Interval type-2 relational analysis and its application to multiple attribute decision making

In this paper, we present the interval type-2 fuzzy rational degree to measure the similarity of the interval type-2 fuzzy sets and apply it to multiple attribute decision making with interval type-2 fuzzy information. First, we introduce the concept of the interval type-2 fuzzy metric spaces, which include interval type-2 fuzzy distance space and interval type-2 fuzzy inner product space, respectively. Based on which, we derive the distance measure and inner product of interval type-2 fuzzy sets, respectively. Then, we introduce the axiomatic definition of the interval type-2 fuzzy rational degree and propose an interval type-2 fuzzy rational degree formula. Moreover, we construct the mathematical optimal model based on two types of interval type-2 fuzzy measures (center of gravity and fuzziness) to determine the optimal attribute weights. Based on the interval type-2 fuzzy rational degree and the optimal weights solution model we proposed, an approach to multiple attribute decision making under interval type-2 fuzzy environment is developed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of our method.