Al-Quran Ashraf, Hassan Nasruddin
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia.
Entropy (Basel). 2018 Jan 31;20(2):101. doi: 10.3390/e20020101.
This paper introduces a novel soft computing technique, called the complex neutrosophic soft expert relation (CNSER), to evaluate the degree of interaction between two hybrid models called complex neutrosophic soft expert sets (CNSESs). CNSESs are used to represent two-dimensional data that are imprecise, uncertain, incomplete and indeterminate. Moreover, it has a mechanism to incorporate the parameter set and the opinions of all experts in one model, thus making it highly suitable for use in decision-making problems where the time factor plays a key role in determining the final decision. The complex neutrosophic soft expert set and complex neutrosophic soft expert relation are both defined. Utilizing the properties of CNSER introduced, an empirical study is conducted on the relationship between the variability of the currency exchange rate and Malaysian exports and the time frame (phase) of the interaction between these two variables. This study is supported further by an algorithm to determine the type and the degree of this relationship. A comparison between different existing relations and CNSER to show the ascendancy of our proposed CNSER is provided. Then, the notion of the inverse, complement and composition of CNSERs along with some related theorems and properties are introduced. Finally, we define the symmetry, transitivity and reflexivity of CNSERs, as well as the equivalence relation and equivalence classes on CNSESs. Some interesting properties are also obtained.
本文介绍了一种新颖的软计算技术，称为复中智软专家关系（CNSER），用于评估两种称为复中智软专家集（CNSESs）的混合模型之间的交互程度。CNSESs用于表示不精确、不确定、不完整和不确定的二维数据。此外，它有一种机制，可将参数集和所有专家的意见整合到一个模型中，因此非常适合用于时间因素在确定最终决策中起关键作用的决策问题。文中定义了复中智软专家集和复中智软专家关系。利用所引入的CNSER的性质，对货币汇率波动与马来西亚出口之间的关系以及这两个变量之间相互作用的时间框架（阶段）进行了实证研究。该研究进一步得到了一种确定这种关系的类型和程度的算法的支持。给出了不同现有关系与CNSER之间的比较，以展示我们所提出的CNSER的优势。然后，介绍了CNSER的逆、补和合成的概念以及一些相关定理和性质。最后，我们定义了CNSER的对称性、传递性和自反性，以及CNSESs上的等价关系和等价类。还获得了一些有趣的性质。
