JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 108-117.doi: 10.6040/j.issn.1671-9352.0.2022.343

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Prime hesitant fuzzy filters in fuzzy implication algebras and its spectral spaces

Chunhui LIU()   

  1. School of Educational Science, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Received:2022-06-23 Online:2023-12-20 Published:2023-12-19

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Abstract:

In this paper, filters problem of fuzzy implication algebras is further studied by using the method and principle of hesitant fuzzy sets and topology. Firstly, the notion of prime hesitant fuzzy filter in fuzzy implication algebras is introduced and its properties are investigated. The prime hesitant fuzzy filter theorem is established and proved of upper semilattice fuzzy implication algebras. Secondly, a topology τ is constructed on the set PHFil (X) consisting of all prime hesitant fuzzy filters in a given fuzzy implication algebra (X, →, 0), a base is obtained of the topology τ and it is proved that the topological space (PHFil(X), τ) is a T0 space.

Key words: fuzzy logic, fuzzy implication algebra, prime hesitant fuzzy filter, spectral space

CLC Number: 

  • O141.1

Table 1

Definition of the implicative operator → on X"

→ 0 a b 1
0 1 1 1 1
a 0 1 1 1
b 0 b 1 1
1 0 a b 1
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