The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (Rl-monoids) are common generalizations of BL-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain i...

In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈∨q)fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established.

We show that an ideal I of an MV -algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I = {0} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combin...

The main aim of this work is to introduce and study the notions ideal direct product d-algebras, d-ideal sub-direct edge positive implicative d-algebras investigate their characterizations.

Doubt m-polar subalgebras (ideals) were introduced and some properties investigated. Also, doubt positive implicative (commutative) ideals defined related results proved.

The fuzzy p-ideals, fuzzy H-ideals and fuzzy BCI-positive implicative ideals of BCI-algebras are studied, and related properties are investigated. We also give some characterizations of these ideals. Mathematics Subject Classifications (2000). 03G25, 06F35, 06B99

This study focuses on combining the theories of m -polar fuzzy sets over id="M2"> BCK -algebras and establishing a new framework id="M3"> id="M4"> -algebras. In this paper, we define idea id="M5"> positive implicative ideals in id="M6"> investigate some related properties. Then, introduce concepts id="M7">...

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...