On open problems based on fuzzy filters of pseudo BCK-algebras

Wang, Wei; Wan, Hui; Kai, Du; Xu, Yang

doi:10.3233/ifs-151938

Cited by 2 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let F be a nonempty subset of a BL-algebra A. Then F is a filter of A if and only if the following conditions hold ID:p1160 (1) 1 ∈ F, ID:p1165 (2) x, x → y ∈ F implies y ∈ F.…”

Section: Id:p1155mentioning

confidence: 99%

See 1 more Smart Citation

Further Complete Solutions to Four Open Problems on Filter of Logical Algebras

Wang¹,

Yang²,

Yang³

2019

IJCIS

View full text Add to dashboard Cite

This paper focuses on the investigation of filters of pseudo BCK-algebra and BL-algebra, important and popular generic commutative and non-commutative logical algebras. By characterizing Boolean filter and implicative filter in pseudo BCK-algebra, the essential equivalent relation between these two filters is revealed. An open problem that "In pseudo BCK-algebra or bounded pseudo BCK-algebra, is the notion of implicative pseudo-filter equivalent to the notion of Boolean filter?" is solved. Based on this, this paper explores the essential relations between the implicative (Boolean) filter and implicative pseudo BCK-algebra. A complete solution to an open problem that "Prove or negate that pseudo BCK-algebras is implicative BCK-algebras if and only if every filter of them is implicative filters (or Boolean filter)" is derived. This paper further characterizes the fantastic filter and normal filter in BL-algebra, then gets the equivalent relation between the two filters, and completely solves two open problems regarding the relationship between these two filters: 1. Under what suitable condition a normal filter becomes a fantastic filter? and 2. (Extension property for a normal filter) Under what suitable condition extension property for normal filter holds?

show abstract

“…Let F be a nonempty subset of a BL-algebra A. Then F is a filter of A if and only if the following conditions hold ID:p1160 (1) 1 ∈ F, ID:p1165 (2) x, x → y ∈ F implies y ∈ F.…”

Section: Id:p1155mentioning

confidence: 99%

“…Let F be a filter of a BL-algebra A. Then the followings are equivalent for all x, y, z ∈ A: ID:p1380 (1) F is a fantastic filter, ID:p1385 (2)…”

Section: Id:p1375mentioning

confidence: 99%