Fuzzy commutative ideals of BCK-algebras

Some kinds of (∈γ,∈γ∨qδMa1, Zhan2, Jun3 2011Computers & Mathematics with Applications20010View full textAdd to dashboardCite

“…It is now natural to investigate similar type of generalizations of the existing fuzzy subsystems with other algebraic structures. With this objective in view, Jun and Meng [9] introduced the concept of (α, β)-fuzzy ideals of a BCK/BCI-algebra and investigated related results. Davvaz [29] applied this theory to near-rings and obtained some useful results.…”

“…They were introduced by Imai and Iséki [3,4] and have been extensively investigated by many researchers; see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. BCI-algebras are generalizations of BCK-algebras.…”

Derivations of Fuzzy Implicative Ideals

“…[9] Let µ be a fuzzy ideal of a BCI-algebra X. Then x * y ≤ z implies µ(x) ≥ min{µ(y), µ(z)}for all x; y; z ∈ X.…”

“…Fuzzy commutative ideals and fuzzy positive implicative ideals studied by Jun and Roh and Jun et al respectively [9], [11].Furthermore, fuzzy implicative ideals and the relation between fuzzy implicative ideals and both commutative and positive implicative ideals was introduced by Meng et al in [15].The concept of derivation which applied firstly on rings and near rings presented by so many authors in [3,4,12,17].Subsequently, Jun and Xin in [10] proposed derivation on BCI-algebra and many results were obtained.Recently, Aboujabal and Alshehri in [1] discussed the derivation on BCK-algebra. Moreover, in 2007 [2] they defined a left derivation in BCI-algebras and investigated a regular left derivation.…”

Commutative Energetic Subsets of BCK-Algebras

“…A fuzzy set f in a BCK-algebra X is called a fuzzy commutative ideal (see [4]) of X if it satisfies (2.9) and (∀x, y, z ∈ X) (f (x * (y * (y * x))) ≥ min{f ((x * y) * z), f (z)}) . (2.12) For a fuzzy set f in X and t ∈ [0, 1], the (strong) upper (resp.…”