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...

BCK-modules were introduced as an action of a BCK-algebra over Abelian group. Homomorphisms form exact sequence which is called BCK-sequence. In this paper, we study homomorphisms BCK-modules. We show that have module structure. Moreover, sequences Hom functors are BCK-sequences.

In this work, we show that single input single output (SISO) fuzzy inference systems based on Fuzzy Relational Inference (FRI) with implicative interpretation of the rule base are universal approximators under suitable choice of operations for the other components of the fuzzy system. The presented proofs make no assumption on the form or representations of the considered fuzzy implications and...

Cantor's naive set theory is characterized by the unrestricted comprehension principle, saying that for every formula A(x), there exists a set {x|A(x)} such that A(t) ↔ t ∈ {x|A(x)} for any term t. The theory is intuitive, elegant, powerful, but unfortunately inconsistent (as witnessed by Russell's paradox). While it is common to somehow restrict the comprehension scheme (as in ZFC), there is a...

The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real an...

As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (c...