Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory of decision making with HFLPR, the paper introduces an algorithm for group decision making with HFLPRs based on the acceptable consistency and consensus measurements, which involves (1) defining a hesitant fuzzy linguistic geometric consistency index (HFLGCI) and proposing a procedure for consistency checking and inconsistency improving for HFLPR; (2) measuring the group consensus based on the similarity between the original individual HFLPRs and the overall perfect HFLPR, then establishing a procedure for consensus ensuring including the determination of decision-makers weights. The convergence and monotonicity of the proposed two procedures have been proved. Some experiments are furtherly performed to investigate the critical values of the defined HFLGCI, and comparative analyses are conducted to show the effectiveness of the proposed algorithm. A case concerning the performance evaluation of venture capital guiding funds is given to illustrate the availability of the proposed algorithm. As an application of our work, an online decision-making portal is finally provided for decision-makers to utilize the proposed algorithms to solve decision-making problems.

翻译：为增强与HFLPR的决策理论,本文件根据可接受的一致性和协商一致的测量结果,引入了与HFLPR集团决策的算法,其中涉及(1) 界定一个模糊的模糊语言几何一致性指数(HFLGCI),并提议一个程序,用以对HFLPR进行一致性检查和改进不一致性;(2) 衡量基于原始个人HFLPR和整体完美的HFLPR之间的相似性的集团共识,然后建立一个协商一致程序,确保包括决策者权重的确定; 已经证明拟议的两个程序的趋同性和单一性; 进一步进行了一些实验,以调查定义的HFLLGCI的关键价值,并进行了比较分析,以表明拟议的算法的有效性; 提供了风险资本指导基金业绩评估案例,以说明拟议的算法的可用性; 作为我们工作的应用,最后为决策者提供了一个在线决策门户,以利用拟议的算法解决决策问题。