The aim of this paper is to apply the concept of interval-valued intuitionistic fuzzy set to implicative ideals and commutative ideals in BCK-algebras and introduced the new notion of interval-valued intuitionistic fuzzy implicative ideals in BCK-algebras and interval-valued intuitionistic fuzzy commutative ideals in BCK-algebras and related properties are investigated.

Matthew Spinks [35] introduces implicative BCSK-algebras, expanding implicative BCK-algebras with an additional binary operation. Subdirectly irreducible implicative BCSK-algebras can be viewed as flat posets with two operations coinciding only in the 1and 2-element cases, each, in the latter case, giving the two-valued implication truth-function. We introduce the resulting logic (for the gener...

The concept of quasi-coincidence of an interval valued fuzzy set is considered. By using this idea, the notion of interval valued (α, β)−fuzzy sub-implicative ideals of BCIalgebras is introduced, which is a generalization of a fuzzy sub-implicative ideal. Also some related properties are studied and in particular, the interval valued (∈,∈ ∨q)−fuzzy subimplicative ideals in a BCI-algebra will be...

A method for studying cognitive conflicts using the repertory grid technique is presented. By means of this technique, implicative dilemmas can be identified, cognitive structures in which a personal construct for which change is wished for implies undesirable change on another construct. We assessed the presence of dilemmas and the severity of symptoms in 46 participants who met criteria for d...

In this note first we define the notions of intuitionistic fuzzy dual positive implicative hyper K-ideals of types 1,2,3,4 and intuitionistic fuzzy dual hyper K-ideals. Then we give some classifications about these notions according to the level subsets. Also by given some examples we show that these notions are not equivalent, however we prove some theorems which show that there are some relat...

In knowledge representation by fuzzy rule based systems two reasoning mechanisms can be distinguished: conjunction-based and implication-based inference. Both approaches have complementary advantages and drawbacks depending on the structure of the knowledge that should be represented. Implicative rule bases are less sensitive to incompleteness of knowledge. However, implication-based inference ...

In this paper, we introduce the notion of n-fold (P, implicative, normal and fantastic) ideals in BCH-algebras which is a natural generalization of notion of (P, implicative, normal and fantastic) ideals in BCH-algebras and we stated and proved some theorems which determine the relationship between these notions.

We describe weak BCC-algebras (also called BZ-algebras) in which the condition (xy)z = (xz)y is satisfied only in the case when elements x, y belong to the same branch. We also characterize branchwise commutative and branchwise implicative weak BCC-algebras satisfying this condition. We also describe connections between various types of implicative weak BCC-algebras.