Journal of Hyperstructures
Volume:11 Issue: 1, Winter and Spring 2022

In this article, we introduce the notion of a (λ, µ)-antifuzzy fields and a (λ, µ)-anti-fuzzy linear spaces over a (λ, µ)-antifuzzy fields and obtain some fundamental properties. Furthermore, we propose the direct product of a (λ, µ)-anti-fuzzy linear spaces and employ it to describe some important properties.

In this paper, we introduce the notion of prime biinterior ideal, bi-interior ideal,strongly prime bi-interior ideal,semiprime strongly irreducible bi-interior ideal and irreducible bi-interior ideal.we study these ideals properties and relation between them and also characterize regular Γ-semiring and Γ-semiring using prime bi-interior ideals.

For a given multilattice M, the set IM of all ideals of M is a complete lattice and for a given complete lattice L, the set FI(M, L) of all L-fuzzy ideals of M is also a complete lattice. The aim of this paper is to characterize L−fuzzy ideals of multilattice and highlight some of their properties based on the Duality Principle. We establish that FI(M, L) is isomorphic to Hom(L ∂ , IM) where L ∂ is the dual of L. Since multilattices generalize lattices, the results remain true for L-fuzzy ideals of lattices.

Let X be a Hausdorff topological vector space over the field of real or complex numbers. When Vietoris topology is given, the hyperspace C(X ) of all nonempty compact subsets of X forms a topological exponential vector space over the same field. Exponential vector space [shortly, evs] is an algebraic ordered extension of vector space in the sense that every evs contains a vector space, and conversely, every vector space can be embedded into such a structure. A semigroup structure, a scalar multiplication and a partial order with some compatible topology comprise the topological evs structure. In this study, we have shown that besides C(X ), there are other hyperspaces namely P(X ), PBal(X ) PCV (X ), PNθ (X ), PS(X ), Pθ(X ) which have the same structure. To characterise the hyperspaces P(X ), C(X ) in light of evs, we have introduced some properties of evs which remain invariant under order-isomorphism. We have also introduced the concept of primitive function of an evs, which plays an important role in such characterisation. Lastly, with the help of these properties, we have characterised C(X ) as well as P(X ) as exponential vector spaces.

Throughout this paper, R is an associative ring (not necessarily commutative) with identity and M is a right R-module with unitary. In this paper, we introduce a new concept of φprime submodule over an associative ring with identity. Thus we define the concept as following: Assume that S(M) is the set of all submodules of M and φ : S(M) → S(M) ∪ {∅} is a function. For every Y ∈ S(M) and ideal I of R, a proper submodule X of M is called φ-prime, if Y I ⊆ X and Y I * φ(X), then Y ⊆ X or I ⊆ (X :R M). Then we examine the properties of φ-prime submodules and characterize it when M is a multiplication module.

In this paper, a hybrid genetic algorithm (HGA) is proposed for the total fuzzy graph coloring (TFGC) problem. TFGC comprises of a graph with fuzzy vertices and edges, seeks to obtain an optimal k−coloring of that fuzzy graph such that the degree of the sum of incompatible vertices and edges is minimized. TFGC is also converted into an equivalent binary programming problem and solved using a CPLEX solver. The performance of both methods is examined on randomly generated fuzzy graphs and computational results are reported. An application based on TFGC is also explored and solved using both proposed methods.

We will show several common fixed point theorems for contraction condition satisfying certain requirements in complex valued intuitionistic fuzzy metric spaces in this study.

The purpose of this research paper is to show the existence and uniqueness of coincidence and fixed points for more then two functions on new contraction mapping and expansive mapping in b-metric spaces. Also we give several corollaries in such spaces. These results are extend many of the past results and will help to research scholar in their advance works.

In this paper, the researcher proved the best proximity point theorem for Suzuki type mappings in the setting of metric spaces endowed a graph. In particular, some earlier results in the literature on both best proximity theory and metric fixed point theory were enriched, extended, and at last generalized.

The existence or non-existence of warped product quasihemi slant submanifolds in trans para-sasakian manifolds is defined. Then we obtain that there are no proper warped product quasi-hemi slant submanifolds in trans para-sasakian manifolds such that totally geodesic and totally umbilical submanifolds of warped product are proper semi-slant and invariant (or anti-invariant).

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler (α, β)-metric. Consequently, we obtained the non-holonomic frame with the help of α 2 = aij (x)y i y j , one form metric β = bi(x)y i and infinite series of (α, β) metric such as the forms I. ( β 4 (β−α) 2 ) + α 2 = F 2 1 + F 2 2 i.e. sum of the square of infinite series of (α, β)-metric and square of Riemannian metric II. ( β 4 (β−α) 2 ) + β 2 = F 2 1 + F 2 3 i.e. sum of the square of infinite series of (α, β)-metric and square of 1-form metric.

In the present paper we study some properties of the para-Kenmotsu manifold with respect to Zamkovoy connection. We discuss locally φ-symmetric para-Kenmotsu manifold with respect to the Zamkovoy connection. Also, we study Ricci Soliton on paraKenmotsu manifold with respect to Zamkovoy connection. Besides these, we discuss Wi-curvature tensor (i=0,1,2...9) with respect to Zamkovoy connection on para-Kenmotsu manifold.