Some Epistemic Extensions of G\"odel Fuzzy Logic

In this paper, we introduce some epistemic extensions of G\"odel fuzzy logic whose Kripke-based semantics have fuzzy values for both propositions and accessibility relations such that soundness and completeness hold. We adopt belief as our epistemic operator, then survey some fuzzy implications to justify our semantics for belief is appropriate. We give a fuzzy version of traditional muddy children problem and apply it to show that axioms of positive and negative introspections and Truth are not necessarily valid in our basic epistemic fuzzy models. In the sequel, we propose a derivation system $K_F$ as a fuzzy version of classical epistemic logic $K$. Next, we establish some other epistemic-fuzzy derivation systems $B_F, T_F, B_F^n$ and $T_F^n$ which are extensions of $K_F$, and prove that all of these derivation systems are sound and complete with respect to appropriate classes of Kripke-based models

Classifications of Hyper Pseudo BCK-algebras of Order 3

In this paper by considering the notion of hyper pseudo BCK-algebra, we classify the set of all non-isomorphic hyper pseudo BCK-algebras of order 3. For this, we define the notion of simple and normalcondition and we characterize the all of hyper pseudo BCK-algebras of order 3 that satisfies these conditions

Rough Set Theory Applied To Hyper BCK-Algebra

The aim of this paper is to introduce the notions of lower and upper approximation of a subset of a hyper BCK-algebra with respect to a hyper BCK-ideal. We give the notion of rough hyper subalgebra and rough hyper BCK-ideal, too, and we investigate their properties

Multivalued linear transformations of hyperspaces

The purpose of this paper is the study of multivalued linear transformations of hypervector spaces (or hyperspaces) in the sense of Tallini. In this regards first we introduce and study various multivalued linear transformations of hyperspaces and then constitute the categories of hyperspaces with respect the different linear transformations of hyperspaces as the morphisms in these categories. Also, we construct some algebraic hyperoperations on Hom K (V,W), the set of all multivalued linear transformations from a hyperspace V into hyperspaces W, and obtaine their basic properties. Finally, we construct the fundamental functor F from HV K , category of hyperspaces over field K into V K , the category of clasical vector space over K

Relation between Hilbert Algebras and BE–Algebras

Hilbert algebras are introduced for investigations in intuitionistic and other non - classical logics and BE -algebra is a generalization of dual BCK -algebra. In this paper, we investigate the relationship between Hilbert algebras and BE -algebras. In fact, we show that a commutative implicative BE -algebra is equivalent to the commutative self distributive BE -algebra, therefore Hilbert algebras and commutative self distributive BE -algebras are equivalent