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

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⎬

Some Generalized Forms of Fuzzy Interval Valued Hyperideals in a Hyperring

Some generalized forms of the hyperideals of a hyperring in the paper of Zhan et al. (2008) will be given. As a generalization of the interval valued (α,β)-fuzzy hyperideals of a hyperring with α,β∈{∈,q,∈∧q,∈∨q} and α≠∈∧q, the notion of generalized interval valued (α,β)-fuzzy hyperideals of a hyperring is also introduced. Special attention is concentrated on the interval valued (∈γ~,∈γ~∨qδ~)-fuzzy hyperideals. As a consequence, some characterizations theorems of interval valued (∈γ~,∈γ~∨qδ~)-fuzzy hyperideals will be provided

Fuzzy hypergroups based on fuzzy relations

AbstractBased on fuzzy reasoning in fuzzy logic, this paper studies a fuzzy hyperoperation and a fuzzy hypergroupoid associated with a fuzzy relation. A sufficient and necessary condition for such a fuzzy hypergroupoid being a fuzzy hypergroup is given, and the properties of the fuzzy hypergroups associated with fuzzy relations are investigated. Furthermore, the definition of normal fuzzy hypergroups is put forward and it is shown that the category NFHG of normal fuzzy hypergroups satisfies all the axioms of topos except for the subobject classifier axiom

A novel method to construct NSSD molecular graphs

A graph is said to be NSSD (=non-singular with a singular deck) if it has no eigenvalue equal to zero, whereas all its vertex-deleted subgraphs have eigenvalues equal to zero. NSSD graphs are of importance in the theory of conductance of organic compounds. In this paper, a novel method is described for constructing NSSD molecular graphs from the commuting graphs of the Hv-group. An algorithm is presented to construct the NSSD graphs from these commuting graphsThis research is partially funded through Quaid-i-Azam University grant URF-201