区间犹豫模糊三角相似度及其多属性群决策

构建了区间犹豫模糊三角相似度公式，并且研究了区间犹豫模糊环境下属性权重信息完全未知的多属性群决策方法。首先基于正弦三角函数构造了区间犹豫模糊三角相似度公式，并证明其满足区间犹豫模糊相似度公理化定义的四个条件；接着给出了区间犹豫模糊交叉熵的公理性定义，同时研究了区间犹豫模糊相似度和区间犹豫模糊交叉熵的关系；最后基于区间犹豫模糊三角相似度，提出了在属性权重信息完全未知条件下的区间犹豫模糊多属性群决策方法，并用实例验证该方法的可行性和有效性。

Interval-valued hesitant fuzzy triangle similarity and its application in multi-attribute group decision making

Interval-valued hesitant fuzzy triangle similarity is constructed, and investigate the multi-attribute group decision making method with attribute weight information is completely unknown under the interval-valued hesitant fuzzy environment. Based on 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. 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. 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.