Kaur Gagandeep, Garg Harish
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, 147004 Punjab, India.
Entropy (Basel). 2018 Jan 17;20(1):65. doi: 10.3390/e20010065.
Cubic intuitionistic fuzzy (CIF) set is the hybrid set which can contain much more information to express an interval-valued intuitionistic fuzzy set and an intuitionistic fuzzy set simultaneously for handling the uncertainties in the data. Unfortunately, there has been no research on the aggregation operators on CIF sets so far. Since an aggregation operator is an important mathematical tool in decision-making problems, the present paper proposes some new Bonferroni mean and weighted Bonferroni mean averaging operators between the cubic intuitionistic fuzzy numbers for aggregating the different preferences of the decision-maker. Then, we develop a decision-making method based on the proposed operators under the cubic intuitionistic fuzzy environment and illustrated with a numerical example. Finally, a comparison analysis between the proposed and the existing approaches have been performed to illustrate the applicability and feasibility of the developed decision-making method.
立方直觉模糊（CIF）集是一种混合集，它可以包含更多信息，以便同时表达区间值直觉模糊集和直觉模糊集，从而处理数据中的不确定性。遗憾的是，到目前为止尚未有关于CIF集上的聚合算子的研究。由于聚合算子是决策问题中的一种重要数学工具，因此本文提出了一些新的立方直觉模糊数之间的Bonferroni均值和加权Bonferroni均值平均算子，用于聚合决策者的不同偏好。然后，我们在立方直觉模糊环境下基于所提出的算子开发了一种决策方法，并通过一个数值例子进行说明。最后，对所提出的方法与现有方法进行了比较分析，以说明所开发决策方法的适用性和可行性。
