Concept lattices and order in fuzzy logic

Intersection-Soft Ideals in Ci-Algebras

“…Combining this and (3.4), we havef (x * a) =f (1), that is, x * a ∈ I. For any (1) and so thatf ((a * (b * x)) * x) =f (1).…”

“…However, philosophers and recently computer scientists as well as other researcher have become interested in vague concepts [1][2][3][4][10][11][12]. One of them, Hájek [3] introduced a BL-algebra which is an algebraic structure for many valued logic.…”

“…One of them, Hájek [3] introduced a BL-algebra which is an algebraic structure for many valued logic. Many researchers investigated the various algebraic structures as MV-algebras, BCK-algebras, BE-algebras and CI-algebras [1][2][3][4][5][6]12]. As a generalization of a BCK-algebra, Kim and Kim [6] introduced the notion of a BE-algebra, and investigated several properties.…”

Scott convergence and fuzzy Scott topology on L-posets

“…In [17,18], an L-preordered set is defined to be a triple .X; R; /, where is an L-equality on X and R is an L-preorder on X which is compatible with . It is verified in [18,22] that if R is compatible with , it must hold that D R^R op . Thus, the L-equality is completely determined by R, so it can be omitted in the definition.…”

“…Fan and Zhang [15,16] studied quantitative domain via fuzzy set theory, where fuzzy partial order was clearly proposed. After analysis, it is easily seen that -categories could be regarded as a fuzzy preordered set in [15,16], and a fuzzy partial ordered set (an L-poset) is equivalent to an L-ordered set introduced by Bělohlávek [17,18]. Later on, Lai and Zhang [19,20] studied complete and directed-complete -categories, and their continuity was also discussed.…”