Fuzzy (weak) implicative hyper K-ideals are introduced, and relations among fuzzy weak implicative hyper K-ideals, fuzzy implicative hyper K-ideals and fuzzy hyper K-ideals are discussed.

Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF -)F -soft lattice implication algebras) are introduced. Basic properties of (IF -)F -soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(∈,∈ ∨qk)((∈,∈ ∨ qk))-fuzzy (...

The notion of intuitionistic fuzzy positive implicative hyper BCK-ideals of type-1, 2... 8 of hyper BCK-algebras was introduced in 2012 by Durga Prasad, Satyanarayana and Ramesh. In this paper, we investigate some related properties of intuitionistic fuzzy positive implicative hyper BCK-ideals of types-1. We characterize positive implicative Artinian (shortly, PI-Artinian) hyper BCK-algebras of...

The notion of n-fold positive implicative filter in a lattice implication algebra is introduced, and related properties are investigated. Relations among a filter, an n-fold implicative filter and an n-fold positive implicative filter are stated. Characterizations of n-fold positive implicative filter are given, and the extension property for n-fold positive implicative filter is established.

In this paper, we introduce the notion of bi-Smarandache BL-algebra, bi-weak Smarandache BL-algebra, bi-Q-Smarandache ideal and bi-Q-Smarandache implicative filter, we obtain some related results and construct quotient of bi-Smarandache BL-algebras via MV-algebras (or briefly bi-Smarandache quotient BL-algebra) and prove some theorems. Finally, the notion of bi-strong Smarandache BL-algebra is ...

The setting of this research is Bishop’s constructive mathematics. Following ideas of Chan and Shum, exposed in their famous paper “Homomorphisms of implicative semigroups”, we discuss the structure of implicative semigroups on sets with tight apartness. Moreover, we use anti-orders instead of partial orders. We study concomitant issues induced by existence of apartness and anti-orders giving s...

We discuss the n-fold implicative/fantastic filters in lattice implication algebras, which are extended notions of implicative/fantastic filters. Characterizations of n-fold implicative/fantastic filters are given. Conditions for a filter to be n-fold implicative are provided. Extension property for an n-fold fantastic filter is established.

The notion of a positive implicative pseudo-valuation on a BCKalgebra is introduced, and its characterizations are investigated. The relationship between a pseudo-valuation and a positive implicative pseudovaluation is examined. Reduction property for a positive implicative pseudo-valuation is established. Mathematics Subject Classification: 06F35, 03G25

We consider the notion of intuitionistic fuzzy n-fold positive implicative ideals in BCI-algebras. We analyse many properties of intuitionistic fuzzy n-fold positive implicative ideals. We also establish extension properties for intuitionistic fuzzy n-fold positive implicative ideals in BCI-algebras. This work generalizes the corresponding results in the crisp case. 2000 Mathematics Subject cla...

Negative self-views have proved to be a consistent marker of vulnerability for depression. However, recent research has shown that a particular kind of cognitive conflict, implicative dilemma, is highly prevalent in depression. In this study, the relevance of these conflicts is assessed as compared to the cognitive model of depression of a negative view of the self. In so doing, 161 patients wi...