New inclusion relation of neutrosophic sets with applications and related lattice structure
New inclusion relation of neutrosophic sets with applications and related lattice structure
复制标题
中智集合的新包含关系及其应用和相关格结构
DOI：
10.1007/s13042-018-0817-6
复制
发表时间：
2018
影响因子：
5.6
通讯作者：
Dai Jianhua
中科院分区：
文献类型：
--
作者：
Zhang Xiaohong;Bo Chunxin;Smar;ache Florentin;Dai Jianhua
本文的主要目的是研究中性集的包含关系及其在多属性决策中的应用。首先，分析了中性粒细胞集合现有的两种包含关系定义（分别称为1型和2型包含关系），并通过实例说明了1型和2型包含关系的不足之处（实际上这是两种极端情况）。其次，引入了中性粒细胞集合包含关系的新定义（称为3型包含关系），并给出了中性粒细胞集合排序的新方法。通过在多属性决策中的应用实例，说明了排序方法的有效性。最后，系统地研究了中性粒细胞集合的3型包含关系和相关的格结构，给出了3型并运算和3型交运算的定义，并证明了以下重要结果：所有基于确定域的中性粒细胞集合就3型并运算、3型交运算和补运算构成一个广义De Morgan代数（非分配格）。由此，从理论上阐明了中性集与模糊集（以及直觉模糊集）的本质区别。
The main purpose of this paper is to study the inclusion relations of neutrosophic sets and some applications in multiple attribute decision making. At first, the existing two definitions of inclusion relation (called type-1 and type-2 inclusion relation, respectively) of neutrosophic sets are analyzed, and the deficiencies of type-1 and type-2 inclusion relations are illustrated by examples (in fact, they are actually two extreme cases). Second, a new definition of inclusion relation of neutrosophic sets (call it type-3 inclusion relation) is introduced, and a new method of ranking of neutrosophic sets is given. The effectiveness of the ranking method is presented by some application examples in multiple attribute decision making. Finally, type-3 inclusion relation of neutrosophic sets and related lattice structure are investigated in a systematic way, the definitions of type-3 union and type-3 intersection operations are proposed, and the following important result is proved: all of neutrosophic sets based on a certainty domain constitute a generalized De Morgan algebra (non-distributive lattice) with respect to type-3 union, type-3 intersection and complement operations. From this, the essential difference between neutrosophic set and fuzzy set (and intuitionistic fuzzy set) is clarified theoretically.