Recently, multi-attribute decision making (MADM) approaches concerning decision maker’s psychological behaviors have received increasing attention, but few of them have taken all the criteria interactions (positive, negative and dependent interactions) into consideration. In this paper, we combine the TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method with the 2-additive fuzzy measure and Choquet integral theory to demonstrate how criteria interactions can be determined and further extend it into intuitionistic fuzzy environment. To begin with, we propose the novel score function and accuracy function to compare the difference among intuitionistic fuzzy sets, which have been proven to be more effective and rational than the existing measure functions. Next, we construct the nonlinear programming model based on maximum-entropy principal to obtain the optimal criteria interactions. Further, 2-additive Choquet-based dominance degree is defined whereby we put forward the 2-additive Choquet integral-based TODIM method under intuitionistic fuzzy environment to handle more challenging MADM problems. Finally, we present results of a didactic example, which concerns selection of suppliers for a manufacturing company, to evaluate the validity and rationality of proposed approach.

中文翻译：

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直觉模糊环境下基于新分数函数和精度函数的扩展TODIM方法

最近，关于决策者心理行为的多属性决策（MADM）方法受到越来越多的关注，但很少有人考虑到所有标准交互（积极、消极和依赖交互）。在本文中，我们将 TODIM（交互和多标准决策的葡萄牙语首字母缩写词）方法与 2-加法模糊测度和 Choquet 积分理论相结合，以演示如何确定标准交互并将其进一步扩展到直觉模糊环境. 首先，我们提出了新颖的评分函数和准确度函数来比较直觉模糊集之间的差异，这已被证明比现有的度量函数更有效和合理。下一个，我们构建了基于最大熵原理的非线性规划模型，以获得最优准则交互作用。此外，定义了基于 2-additive Choquet 的优势度，我们提出了在直觉模糊环境下基于 2-additive Choquet 积分的 TODIM 方法来处理更具挑战性的 MADM 问题。最后，我们展示了一个教学示例的结果，该示例涉及一家制造公司的供应商选择，以评估所提出方法的有效性和合理性。