Cubic intuitionistic fuzzy sets (CIFSs) are a powerful and relevant medium for expressing imprecise information to solve the decision-making problems. The conspicuous feature of their mathematical concept is that it considers simultaneously the hallmarks of both the intuitionistic fuzzy sets (IFSs) and interval-valued IFSs. The present paper is divided into two parts: (i) defining the correlation measures for the CIFSs; (ii) introducing the decision-making algorithm for the CIFS information. Furthermore, few of the fundamental properties of these measures are examined in detail. Based on this, we define a novel algorithm to solve the multi-criteria decision-making process and illustrate numerical examples related to watershed’s hydrological geographical areas, global recruitment problem and so on. A contrastive analysis with several existing studies is also administered to test the effectiveness and verify the proposed method.

三次直觉模糊集（CIFS）是用于表达不精确信息以解决决策问题的强大且相关的媒介。他们的数学概念的显着特征是它同时考虑了直觉模糊集（IFS）和区间值IFS的标志。本文分为两个部分：（i）定义CIFS的相关度量；（ii）引入CIFS信息的决策算法。此外，这些措施的基本性质很少被详细检查。在此基础上，我们定义了一种新颖的算法来解决多准则决策过程，并举例说明了与流域水文地理区域，全球招募问题等有关的数值示例。