Journal of Hyperstructures
Volume:12 Issue: 1, Winter and Spring 2023

The concept of a Γ-semihyperring is a generalization of a semiring, semihyperring, Γ-semiring. In this Paper we introduce the notion of bi-interior Γ-hyperideals, quasi-interior Γ-hyperideals and bi-quasi-interior Γ-hyperideals in a Γ- semihyperring as a generalization of Γ-hyperideal, left-Γ-hyperideal, right-Γ- hyperideals, bi Γ-hyperideal, quasi Γ-hyperideal, interior Γ-hyperideals of Γ-semihyperring. We studied the properties of these Γ-hyperideals and characterized them in simple Γ-semihyperring and regular Γ-semihyperring.

In this paper, we study the notion of semi-derivation in Krasner hyperring and present some examples of them. We introduce the concept of generalized semi-derivation in Krasner hyperring and present some examples. Then, we derive some properties of semi-derivation on Krasner hyperring which proves the commutativity of a Krasner hyperring. Later we prove if f is a non-zero semi-derivation on Krasner hyperring R, then f2≠ 0 on R. Finally, for a generalized semi-derivation F on R, if F(u o v)=0, for all u,v∈ I, then R is commutative.

In this paper, we have introduced and studied the notion of a fuzzy independent pair and obtain some properties of fuzzy α-modular pairs and independent pairs.

This article presents the novel set termed SB-neutrosophic set (SB-NSS), which extends the concept of the Neutrosophic set (NSS). We illustrate its fundamental operations with examples. This concept of SB-NSSs is applied to BCK/BCI-algebras, and we introduce the notion of SB-neutrosophic subalgebra (SB-NSSA), SB-neutrosophic ideal (SB-NSI), and related properties are investigated. Furthermore, we provide conditions for an SB-NSS to be an SB-NSSA, for an SB-NSS to be an SB-NSI, and for an SB-NSSA to be an SB-NSI. In a BCI-algebra, conditions for an SB-NSI to be an SB-NSSA are given.

We consider the notion of fuzzy lattices introduced by Chon and define a fuzzy semi-ortholattice and a fuzzy semi-orthocomplemented lattice. We investigate some algebraic properties of these fuzzy lattices such as a sufficient condition of a fuzzy semi-lattice and the equivalent relationship between fuzzy covering property and fuzzy exchange property in fuzzy lattices.

In this paper, the concept of soft neighborhood of an element in a soft topological space is introduced, and its basic properties are studied.

In order to create a dynamic measure that describes distances between spatiotemporal points whose positions change over time as well as between the data represented by these points, a temporal intuitionistic fuzzy metric space is created in this paper. The notions of temporal fuzzy t-norm, temporal fuzzy t-conorm, and temporal fuzzy negation which have not previously been discussed in the literature are defined, and some of their fundamental characteristics are investigated, in order to define this new method.The idea that the degrees of nearness and non-nearness change with time is the basis for a novel definition of the concept of temporal intuitionistic fuzzy metric spaces. However, the basic topological characteristics of the temporal intuitionistic fuzzy metric space are also looked at. We demonstrate how this new temporal metric space preserves the basic characteristics offered by both classical and fuzzy metric spaces. As a result, a new, more flexible, and dynamic metric topology is created while maintaining the fundamental topological characteristics of fuzzy and intuitionistic fuzzy metric spaces.

In this paper, we have proved fixed point results for multi-valued Suzuki nonexpansive mappings in complete hyperbolic spaces along with application.

Let $\mathcal{A}$ be a Banach algebra with unity $1$, and $\theta:\mathcal{A}\rightarrow \mathcal{A}$ be an continuous automorphism. In this paper we characterize a continuous linear map $T: \mathcal{A}\rightarrow \mathcal{A}$ which satisfies one of the following conditions:\[a,b\in \mathcal{A}, \, ab =w\Longrightarrow \theta(a)T(b)=T(w) ,\]\[ a,b \in \mathcal{A}, \, ab =w\Longrightarrow T(a)\theta(b)=T(w) ,\]or\[ a,b \in \mathcal{A}, \, ab =w\Longrightarrow \theta(a)T(b)=T(a)\theta(b)=T(w) ,\]where $w\neq 0$ is a left (right) separating point of $\mathcal{A}$.

Uncertain linear systems are defined and these linear systems using Log-normal and Zigzag variables based on their inverse distributions are investigated. A method for solving Log-normal and Zigzag linear uncertain devices has been designed and conditions for the existence of an uncertain linear has been provided. To show the effectiveness of the proposed method, two examples are given. Finally, a diet is presented to demonstrate the scientific importance of uncertain linear systems.

In this paper, we study the geometry of warped product semi invariant submanifold of a nearly $(\varepsilon, \delta )$-trans-Sasakian manifold $ M$ with a quarter symmetric non metric connection. We see that warped product of the type$ E_{\perp}{\times}{_{y}}{E}_{T}$ is a usual Riemannian product of $ E_{\perp} $ and $ E_{T}$ , where $ E_{\perp}$ and $ E_{T} $ are anti-invariant and invariant submanifolds of a nearly $(\varepsilon, \delta )$-trans-Sasakian manifold with a quarter symmetric non metric connection $ M$, respectively. We also obtain a characterization for such type of warped product.

R. Miron initiated the study of L-duality in Lagrange and Finsler spaces in 1987. The concrete L-duals of the Randers metric, Kropina metric, Matsumoto metric, exponential metric, as well as a few more unique (α, β)-metrics, are really just an of the remarkable results obtained. The importance of L-duality, however, is basically limited to finding the dual of a few key Finsler functions.In this paper, we find L-dual of a Finsler space with a special (α, β)-metric $ F=\frac{(\alpha+\beta)^3}{\alpha^2}$, where α is a Riemannian metric and β is a differential one form.