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Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications

School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China
School of Mathematics Science, Liaocheng University, Liaocheng 252000, China
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 910;
Received: 17 May 2019 / Revised: 20 June 2019 / Accepted: 25 June 2019 / Published: 12 July 2019
PDF [744 KB, uploaded 12 July 2019]


Multi-attribute decision-making (MADM) is a part of management decision-making and an important branch of the modern decision theory and method. MADM focuses on the decision problem of discrete and finite decision schemes. Uncertain MADM is an extension and development of classical multi-attribute decision making theory. When the attribute value of MADM is shown by neutrosophic number, that is, the attribute value is complex data and needs three values to express, it is called the MADM problem in which the attribute values are neutrosophic numbers. However, in practical MADM problems, to minimize errors in individual decision making, we need to consider the ideas of many people and synthesize their opinions. Therefore, it is of great significance to study the method of attribute information aggregation. In this paper, we proposed a new theory—non-dual multi-granulation neutrosophic rough set (MS)—to aggregate multiple attribute information and solve a multi-attribute group decision-making (MGDM) problem where the attribute values are neutrosophic numbers. First, we defined two kinds of non-dual MS models, intersection-type MS and union-type MS. Additionally, their properties are studied. Then the relationships between MS, non-dual MS, neutrosophic rough set (NRS) based on neutrosophic intersection (union) relationship, and NRS based on neutrosophic transitive closure relation of union relationship are outlined, and a figure is given to show them directly. Finally, the definition of non-dual MS on two universes is given and we use it to solve a MGDM problem with a neutrosophic number as the attribute value. View Full-Text
Keywords: multi-granulation neutrosophic rough set; non-dual; two universes; multi-attribute group decision making multi-granulation neutrosophic rough set; non-dual; two universes; multi-attribute group decision making

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Bo, C.; Zhang, X.; Shao, S. Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications. Symmetry 2019, 11, 910.

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