Several Generalized Interval-Valued 2-Tuple Linguistic Interval Distance Measures and Their Application

Interval-valued linguistic variables are efficient tools to express the decision makers' uncertain qualitative judgments. Considering the application of interval-valued linguistic variables, this paper proposes an interval distance measure, which is then used to define interval-valued linguistic interval distance measures by combining the 2-tuple linguistic representation model. To reflect the interactions between elements in a set, three correlative interval distance measures on interval valued linguistic variables are proposed. Meanwhile, several models designed to obtain the optimal weighting vector are constructed. After that, an approach to pattern recognition and to multi-attribute decision making with interval-valued linguistic information is developed. Meanwhile, associated examples are offered to demonstrate the concrete application of the proposed procedure.