Abu Qamar Majdoleen, Hassan Nasruddin
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia.
Entropy (Basel). 2018 Mar 6;20(3):172. doi: 10.3390/e20030172.
Q-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems. Relations are a suitable tool for describing correspondences between objects. In this study we introduce and discuss Q-neutrosophic soft relations, which can be discussed as a generalization of fuzzy soft relations, intuitionistic fuzzy soft relations, and neutrosophic soft relations. Q-neutrosophic soft relation is a sub Q-neutrosophic soft set of the Cartesian product of the Q-neutrosophic soft sets, in other words Q-neutrosophic soft relation is Q-neutrosophic soft sets in a Cartesian product of universes. We also present the notions of inverse, composition of Q-neutrosophic soft relations and functions along with some related theorems and properties. Reflexivity, symmetry, transitivity as well as equivalence relations and equivalence classes of Q-neutrosophic soft relations are also defined. Some properties of these concepts are presented and supported by real life examples. Finally, an algorithm to solve decision making problems using Q-neutrosophic soft relations is developed and verified by an example to show the efficiency of this method.
Q-中性软集本质上是由三个独立的二维隶属函数表征的中性软集，这三个函数分别代表不确定性、不定性和伪性。因此，它可应用于大多数实际问题中出现的二维不精确、不确定和不一致的数据。关系是描述对象之间对应关系的合适工具。在本研究中，我们引入并讨论了Q-中性软关系，它可作为模糊软关系、直觉模糊软关系和中性软关系的推广来进行讨论。Q-中性软关系是Q-中性软集的笛卡尔积的一个子Q-中性软集，换句话说，Q-中性软关系是全域笛卡尔积中的Q-中性软集。我们还给出了Q-中性软关系和函数的逆、合成的概念以及一些相关定理和性质。还定义了Q-中性软关系的自反性、对称性、传递性以及等价关系和等价类。这些概念的一些性质通过实际例子给出并得到支持。最后，开发了一种使用Q-中性软关系解决决策问题的算法，并通过一个例子进行验证，以展示该方法的有效性。
