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.

The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

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...

We propose a novel semantics for positive abductive logic programs with implicative integrity constraints, namely integrity constraints in the form of implications. We show that this semantics is better suited to deal with several applications of abductive logic programming. Moreover, we prove that, in the propositional case, the existing abductive proof procedure IFF is sound and “strongly” co...

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...

‎In this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎We show that if F is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎Rad(F)=F‎. ‎We proved the extension theorem for radical of filters in residuated lattices‎. ‎Also‎, ‎we study the radical‎ ‎of filters in linearly o...

In this paper, we introduce the concepts of n-fold obstinate pseudo-hoop and n-fold obstinate filter in pseudo-hoops. Then we investigated these notions and proved some properties of them. Also, we discussed the relationship between n-fold obstinate pseudo-hoop and n-fold obstinate filter and other types of n-fold pseudo-hoops and n-fold filters such as n-fold (positive) implicative filter and ...

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.