Fuzzy implicative and Boolean filters of R0 algebras

Authors:
Liu Lianzhen;Li Kaitai
Affiliations:
College of Science, Xi'an Jiaotong University, 710049 Xi'an, China;College of Science, Xi'an Jiaotong University, 710049 Xi'an, China
Venue:
Information Sciences—Informatics and Computer Science: An International Journal
Year:
2005

Citing 6
Cited 14

L-valued propositional logic Lvpl

Information Sciences: an International Journal
On the logic foundation of fuzzy reasoning

Information Sciences: an International Journal
&agr;-resolution principle based on first-order lattice-valued logic LF (X)

Information Sciences: an International Journal
Quotient structures of some implicative algebras via fuzzy implicative filters

Fuzzy Sets and Systems
Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras

Fuzzy Sets and Systems
ILI-ideals and prime LI-ideals in lattice implication algebras

Information Sciences: an International Journal

TL-filters of integral residuated l-monoids

Information Sciences: an International Journal
Boolean filters and positive implicative filters of residuated lattices

Information Sciences: an International Journal
On v-filters and normal v-filters of a residuated lattice with a weak vt-operator

Information Sciences: an International Journal
Fuzzy filters and fuzzy prime filters of bounded Rl-monoids and pseudo BL-algebras

Information Sciences: an International Journal
On the role of logical connectives for primality and functional completeness of algebras of logics

Information Sciences: an International Journal
Linguistic truth-valued lattice-valued propositional logic system lP(X) based on linguistic truth-valued lattice implication algebra

Information Sciences: an International Journal
Fuzzy hyperrings (Hv-rings) based on fuzzy universal sets

Information Sciences: an International Journal
On filter theory of residuated lattices

Information Sciences: an International Journal
On fuzzy filters of pseudo BL-algebras

Fuzzy Sets and Systems
Stone-like representation theorems and three-valued filters in R0- algebras (nilpotent minimum algebras)

Fuzzy Sets and Systems
Interval-valued $\mathcal{T}$-fuzzy filters and interval-valued $\mathcal{T}$-fuzzy congruences on residuated lattices

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
New representation for filters of BL-algebras

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Falling fuzzy implicative filters of R0-algebras and its applications

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Recent Advances in Soft Computing: Theories and Applications
On filters of R0-algebras connected to intuitionistic fuzzy sets

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

Quantified Score

Hi-index	0.00

Visualization

Abstract

The notions of fuzzy filters, fuzzy implicative filters and fuzzy Boolean filters are introduced in R0 algebras, respectively. Some of their properties are investigated. The relations between fuzzy implicative filters and fuzzy Boolean filters are discussed. The characterizations of fuzzy implicative filters are studied and the following is proved to be equivalent (1) a fuzzy filter f is implicative, (2) f is a fuzzy Boolean filter, (3) ∀x,y,z ∈ L, f(x → z) ≥ f(x → (¬z → y)) ∧ f(y → z), (4) ∀x,y ∈ L, f(x → y) = f(x → (¬y → y)), (5) ∀x ∈ L, n ≥ 1, f(nx) = f(x).