简化中智集的指数熵及其在决策中的应用
Exponential Entropy for Simplified Neutrosophic Sets and Its Application in Decision Making.
作者信息
Ye Jun, Cui Wenhua
机构信息
Department of Electrical and Information Engineering, Shaoxing University, Shaoxing 312000, China.
出版信息
Entropy (Basel). 2018 May 10;20(5):357. doi: 10.3390/e20050357.
Entropy is one of many important mathematical tools for measuring uncertain/fuzzy information. As a subclass of neutrosophic sets (NSs), simplified NSs (including single-valued and interval-valued NSs) can describe incomplete, indeterminate, and inconsistent information. Based on the concept of fuzzy exponential entropy for fuzzy sets, this work proposes exponential entropy measures of simplified NSs (named simplified neutrosophic exponential entropy (SNEE) measures), including single-valued and interval-valued neutrosophic exponential entropy measures, and investigates their properties. Then, the proposed exponential entropy measures of simplified NSs are compared with existing related entropy measures of interval-valued NSs to illustrate the rationality and effectiveness of the proposed SNEE measures through a numerical example. Finally, the developed exponential entropy measures for simplified NSs are applied to a multi-attribute decision-making example in an interval-valued NS setting to demonstrate the application of the proposed SNEE measures. However, the SNEE measures not only enrich the theory of simplified neutrosophic entropy, but also provide a novel way of measuring uncertain information in a simplified NS setting.
熵是用于度量不确定/模糊信息的众多重要数学工具之一。作为中智集（NSs）的一个子类，简化中智集（包括单值和区间值中智集）能够描述不完整、不确定和不一致的信息。基于模糊集的模糊指数熵概念，本文提出了简化中智集的指数熵度量（称为简化中智指数熵（SNEE）度量），包括单值和区间值中智指数熵度量，并研究了它们的性质。然后，将所提出的简化中智集指数熵度量与现有的区间值中智集相关熵度量进行比较，通过一个数值例子来说明所提出的SNEE度量的合理性和有效性。最后，将所开发的简化中智集指数熵度量应用于区间值中智集环境下的多属性决策例子，以展示所提出的SNEE度量的应用。然而，SNEE度量不仅丰富了简化中智熵理论，还提供了一种在简化中智集环境下度量不确定信息的新方法。
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