### Pythagorean fuzzy three-way concept lattice

JI Ru-ya1,2, WEI Ling1,2*, REN Rui-si1,2, ZHAO Si-yu1,2,3

1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xian 710127, Shaanxi, China;
3. College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China
• Published:2020-11-17

Abstract: Pythagorean fuzzy set theory is introduced into fuzzy three-way concept lattice. The construction of Pythagorean fuzzy three-way concept lattice is studied under the Pythagorean fuzzy formal context. First, the relationships between objects and attributes are expressed by the membership degree and non-membership degree combined with the Pythagorean fuzzy set theory. On this foundation, the definition of the Pythagorean fuzzy formal context is given. Next, based on threshold α, β and the idea of three-way decision, the object sets(the attribute sets)are divided into three parts: positive region, negative region and boundary region. On this basis, the definitions and relevant theorems of two kinds of Pythagorean fuzzy three-way concepts(the object induced Pythagorean fuzzy three-way concept and the attribute induced Pythagorean fuzzy three-way concept)are given, and the corresponding Pythagorean fuzzy three-way concept lattices are constructed. Finally, the applications of Pythagorean fuzzy three-way concept lattice in real problems are explained in detail with examples.

CLC Number:

• O29
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