Wang Gang, Zhang Jie, Song Yafei, Li Qiang
Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China.
Aviation Maintenance NCO Academy, Air Force Engineering University, Xinyang 464000, China.
Entropy (Basel). 2018 Dec 17;20(12):981. doi: 10.3390/e20120981.
As the complementary concept of intuitionistic fuzzy entropy, the knowledge measure of Atanassov's intuitionistic fuzzy sets (AIFSs) has attracted more attention and is still an open topic. The amount of knowledge is important to evaluate intuitionistic fuzzy information. An entropy-based knowledge measure for AIFSs is defined in this paper to quantify the knowledge amount conveyed by AIFSs. An intuitive analysis on the properties of the knowledge amount in AIFSs is put forward to facilitate the introduction of axiomatic definition of the knowledge measure. Then we propose a new knowledge measure based on the entropy-based divergence measure with respect for the difference between the membership degree, the non-membership degree, and the hesitancy degree. The properties of the new knowledge measure are investigated in a mathematical viewpoint. Several examples are applied to illustrate the performance of the new knowledge measure. Comparison with several existing entropy and knowledge measures indicates that the proposed knowledge has a greater ability in discriminating different AIFSs and it is robust in quantifying the knowledge amount of different AIFSs. Lastly, the new knowledge measure is applied to the problem of multiple attribute decision making (MADM) in an intuitionistic fuzzy environment. Two models are presented to determine attribute weights in the cases that information on attribute weights is partially known and completely unknown. After obtaining attribute weights, we develop a new method to solve intuitionistic fuzzy MADM problems. An example is employed to show the effectiveness of the new MADM method.
作为直觉模糊熵的互补概念，阿塔纳索夫直觉模糊集（AIFS）的知识测度受到了更多关注，并且仍然是一个开放的课题。知识量对于评估直觉模糊信息很重要。本文定义了一种基于熵的AIFS知识测度，以量化AIFS所传达的知识量。对AIFS中知识量的性质进行了直观分析，以促进知识测度公理定义的引入。然后，我们基于熵散度测度提出了一种新的知识测度，考虑了隶属度、非隶属度和犹豫度之间的差异。从数学角度研究了新的知识测度的性质。通过几个例子来说明新的知识测度的性能。与几种现有的熵和知识测度的比较表明，所提出的知识测度在区分不同的AIFS方面具有更强的能力，并且在量化不同AIFS的知识量方面具有鲁棒性。最后，将新的知识测度应用于直觉模糊环境下的多属性决策（MADM）问题。提出了两个模型，用于在属性权重信息部分已知和完全未知的情况下确定属性权重。在获得属性权重后，我们开发了一种新的方法来解决直觉模糊MADM问题。通过一个例子展示了新的MADM方法的有效性。
