区间犹豫模糊三角相似度及其多属性群决策

Interval-valued hesitant fuzzy triangle similarity is constructed, and we investigate the multi-attribute group decision making problems with attribute weight information is completely unknown under the interval-valued hesitant fuzzy environment. Firstly, based in the sine triangle function, the interval-valued hesitant fuzzy triangle similarity formula is developed, and it proves that the interval-valued hesitant fuzzy triangle similarity satisfies four axiomatic requirements of interval-valued hesitant fuzzy similarity. Secondly, the axiomatic definition of cross-entropy for interval-valued hesitant fuzzy sets is presented, and the relationships between interval-valued hesitant fuzzy similarity measures and interval-valued hesitant fuzzy cross-entropy is studied. Finally, according to the interval-valued hesitant fuzzy triangle similarity, a new method for interval-valued hesitant fuzzy multi-attribute group decision making problems with completely unknown attribute weight information is proposed, and an illustrative example is given to demonstrate its practicality and effectiveness.