Journal of Hyperstructures
Volume:5 Issue: 2, Summer and Autumn 2016

In this paper‮, ‮we define the relations $\beta $ and $\beta^*$ on hyper pseudo $BCK$-algebras and investigate some related properties‮.
‮We give a necessary and sufficient condition for $\beta ^*$ to be regular‮. ‮By using $\beta^*$‮, ‮we make the quotient hyper pseudo $BCK$-algebra‮. ‮Finally‮, ‮by applying the concept of fundamental on pseudo $BCK$-algebra‮, ‮we prove that any pseudo $BCK$-algebra is fundamental‮.

We deal with an hypergroupoid endowed with a relation denoted by “≤”, we call it ≤–hypergroupoid. We prove that a nonempty subset A of a ≤–hypergroupoid H is a prime (resp. semiprime) ideal of H if and only if the characteristic function fA is a fuzzy prime (resp. fuzzy semiprime) ideal of H.

In this paper, we have achieved hyperoperations using soft set theory. We have showed that any given set H is a hyperstructure with And and Or operations in soft set theory. Furthermore, for any given algebraic structure (H,∗), we have created hyperstructure using soft set operation which mentioned by Molodtsov [8] and binary operation ∗.

In this paper, we define the concepts of (good) congruences and strong congruences on hyper lattice implication algebras and use them to construct quotient hyper lattice implication algebras. We describe the relations between hyper lattice implication algebra and hyper MV-algebra, hyper K-algebra, (weak) hyper residuated lattices.

In this paper, we generalized some statistical distributions by using fractional calculus.The domain of parameter space for these distributions was expanded and their PDFs also presented as a product of fractional derivation of Dirac delta function of shape parameter order.

The aim of this paper is to establish some uniqueness and well-posedness results for a general inequality of equilibrium problems type involving α-monotone bifunction, whose solution is sought in a subset K of a Banach space X. Some metric characterizations and sufficient conditions for these types of well-posedness are obtained. Moreover, we prove that the well-posedness of generalized equilibrium problems is equivalent to the existence and uniqueness of its solution.

Mother-infant vocalization from distance in some animal species such as bats, gulls and penguins is a basic tool to find the other’s location. It is referred to echolocation or bio-sonar characteristics which is important for the mother to find exactly its own baby in a large colony. Moreover, the baby uses it to better conduction the mother in getting back to the nest without knowing its exact location. This natural fact is the motivation of the current study to devise a novel metaheuristic algorithm in solving optimization problems. The proposed methodology was tested on some continuous functions and led to promising results on convergence.