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...

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 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.

In this paper, we present the notions of cubic (weak) implicative hyper BCK-ideals of hyper BCKalgebras and then we present some results which characterize the above notions according to the level subsets. In addition, we obtain the relationship among these notions, cubic positive implicative hyper BCK-ideals of types-1, 2...8 and obtain some related results.AMS (2010): 06F35.

The class of radial fuzzy systems is introduced. The fuzzy systems in this class use radial functions to implement membership functions of fuzzy sets and exhibit a shape preservation property in antecedents of their rules. The property is called the radial property. It enables the radial fuzzy systems to have their computational model mathematically tractable under both conjunctive and implicat...

This paper proposes the implicative rating measure developed on the typicality measure. The paper also proposes a new recommendation model presenting the top N items to the active users. The proposed model is based on the user-based collaborative filtering approach using the implicative intensity measure to find the nearest neighbors of the active users, and the proposed measure to predict user...