On Fuzzy Gamma Hypermodules

Let R be a Γ-hyperring and M be an Γ -hypermodule over R. We introduce and tudy fuzzy RΓ -hypermodules. Also, we associate a Γ- hypermodule to every fuzzy Γ-hypermodule and investigate its basic properties

Term Functions and Fundamental Relation of Fuzzy Hyperalgebras

We introduce and study term functions over fuzzy hyperalgebras. We start from this idea that the set of nonzero fuzzy subsets of a fuzzy hyperalgebra can be organized naturally as a universal algebra, and constructing the term functions over this algebra. We present the form of generated subfuzzy hyperalgebra of a given fuzzy hyperalgebra as a generalization of universal algebras and multialgebras. Finally, we characterize the form of the fundamental relation of a fuzzy hyperalgebra

Narrative Language as an Expression of Individual and Group Identity

Scientific Narrative Psychology integrates quantitative methodologies into the study of identity. Its methodology, Narrative Categorical Analysis, and its toolkit, NarrCat, were both originally developed by the Hungarian Narrative Psychology Group. NarrCat is for machine-made transformation of sentences in self-narratives into psychologically relevant, statistically processable narrative categories. The main body of this flexible and comprehensive system is formed by Psycho-Thematic modules, such as Agency, Evaluation, Emotion, Cognition, Spatiality, and Temporality. The Relational Modules include Social References, Semantic Role Labeling (SRL), and Negation. Certain elements can be combined into Hypermodules, such as Psychological Perspective and Spatio-Temporal Perspective, which allow for even more complex, higher level exploration of composite psychological processes. Using up-to-date developments of corpus linguistics and Natural Language Processing (NLP), a unique feature of NarrCat is its capacity of SRL. The structure of NarrCat, as well as the empirical results in group identity research, is discussed

THE TRANSPOSITION AXIOM IN HYPERCOMPOSITIONAL STRUCTURES

The hypergroup (as defined by F. Marty), being a very general algebraic structure, was subsequently quickly enriched with additional axioms. One of these is the transposition axiom, the utilization of which led to the creation of join spaces (join hypergroups) and of transposition hypergroups. These hypergroups have numerous applications in geometry, formal languages, thetheory of automata and graph theory. This paper deals with transposition hypergroups. It also introduces the transposition axiom to weaker structures, which result from the hypergroup by the removal of certain axioms, thus defining the transposition hypergroupoid, the transposition semi-hypergroup and the transposition quasi-hypergroup. Finally, it presents hypercompositional structures with internal or external compositions and hypercompositions, in which the transposition axiom is valid. Such structures emerged during the study of formal languages and the theory of automata through the use of hypercompositional algebra

History and new possible research directions of hyperstructures

We present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research

MULTIVALUED FUNCTIONS, FUZZY SUBSETS AND JOIN SPACES

One has considered the Hypergroupoid Η Γ = associated with a multivalued function Γ from H to a set D, defined as follows:∀ x ∈ H, x ο Γ x = ⎨y⏐ Γ(y) ∩ Γ(x) ≠ ∅⎬ ,∀ (y,z) ∈ H 2 , y ο Γ z = y ο Γ y ∪ z ο Γ z ,and one has calculated the fuzzy grade ∂(Η Γ ) for several functions Γ defined on sets H, such that ⎮H⎮ ∈ ⎨3, 4, 5, 6, 8, 9, 16⎬

Normal Self-injective Hyperrings

       In this paper normal self-injective hyperrings are introduced and studied. Some new relations between this concept and essential hyperideal, dense hyperideal, and divisible hyperring are studied.