Int-soft structures applied to ordered semihypergroups

Molodtsov introduced the theory of soft sets, which canbe seen as a new mathematical approach to vagueness. The main goal of thispaper is to introduce and study some classes of ordered semihypergroups andto investigate some interesting characterizations theorems of these classesin terms of int-soft hyperideals. In this respect, we characterize weaklyregular ordered semihypergroups for example (see Theorems 25, 26 and 28)intra-regular and left weakly-regular ordered semihypergroups (see Theorems30 and 32) and semisimple ordered semihypergroups (see Theorems 37 and 39)in terms of int-soft hyperideals. In this regard, we study semisimpleordered semihypergroups and characterize it in terms of int-softhyperideals. We also characterize intra-regular and weakly-regular orderedsemihypergroups in terms of int-soft hyperideals

Completely simple and regular semi hypergroups

In this paper the notion of simple and completely simple semi hypergroups are introduced. Basic properties of these algebraic structures are considered. Some methods for constructing new kinds of these hyperstructures are presented. The regularity of semi hypergroups is considered and three structural results are proved

Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras in BG-algebras

In this paper, the concepts of intuitionistic fuzzy translation to intuitionistic fuzzy subalgebras in BG-algebras are introduced. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras are introduced and several related properties are investigated. In this paper, the relationships between intuitionistic fuzzy translations and intuitionistic fuzzy extensions of intuitionistic fuzzy subalgebras are investigated.Publisher's Versio

On Rough Hyperideals in Hyperlattices

We introduce and study rough hyperideals in hyperlattices. First, we give some interesting examples of hyperlattices and introduce hyperideals of hyperlattices. Then, applying the notion of rough sets to hyperlattices, we introduce rough hyperideals in hyperlattices, which are extended notions of hyperideals of hyperlattices. In addition, we consider rough hyperideals in Cartesian products and quotients of hyperlattices. Finally, we investigate some properties about homomorphic images of rough hyperideals in hyperlattices

On Ordered (p; q)-Lateral Ideals in Ordered Ternary Semigroups

In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary semigroups. Also, some properties of (p; q)-lateral simple ordered ternary semigroup have been examined. Further, we characterize the relationship between minimal (resp., maximal) ordered (p; q)- lateral ideals and (p; q)-lateral simple ordered ternary semigroups

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⎬