Alhazaymeh Khaleed, Al-Qudah Yousef, Hassan Nasruddin, Nasruddin Abdul Muhaimin
Department of Basic Sciences and Mathematics, Faculty of Science, Philadelphia University, Amman 19392, Jordan.
Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan.
Entropy (Basel). 2020 Aug 31;22(9):963. doi: 10.3390/e22090963.
From the hybrid nature of cubic sets, we develop a new generalized hybrid structure of cubic sets known as cubic vague sets (CVSs). We also define the concept of internal cubic vague sets (ICVSs) and external cubic vague sets (ECVSs) with examples and discuss their interesting properties, including ICVSs and ECVSs under both P and R-Order. Moreover, we prove that the R and R-intersection of ICVSs (or ECVSs) need not be an ICVS (or ECVS). We also derive the different conditions for P-union (P-intersection, R and R-intersection) operations of both ICVSs (ECVSs) to become an ICVS (ECVS). Finally, we introduce a decision-making based on the proposed similarity measure of the CVSs domain and a numerical example is given to elucidate that the proposed similarity measure of CVSs is an important concept for measuring entropy in the information/data. It will be shown that the cubic vague set has the novelty to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature.
基于立方集的混合性质，我们开发了一种新的立方集广义混合结构，称为立方模糊集（CVSs）。我们还通过示例定义了内部立方模糊集（ICVSs）和外部立方模糊集（ECVSs）的概念，并讨论了它们有趣的性质，包括P序和R序下的ICVSs和ECVSs。此外，我们证明了ICVSs（或ECVSs）的R并和R交不一定是ICVS（或ECVS）。我们还推导了ICVSs（ECVSs）的P并（P交、R并和R交）运算成为ICVS（ECVS）的不同条件。最后，我们基于所提出的CVSs域相似性度量引入了一种决策方法，并给出了一个数值示例来说明所提出的CVSs相似性度量是信息/数据中测量熵的一个重要概念。结果表明，立方模糊集具有新颖性，能够准确地表示和建模本质上具有周期性的现实生活现象的二维信息。
