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The intention of this article is to introduce and characterise the concept of preopen sets and prelocally closed sets in Generalised Topology and Minimal structure spaces.

This research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly ℐ -lacunary Cauchy, and strongly ℐ ∗ -lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships. [ABSTRACT FROM AUTHOR]

In this article we introduce the notion of double sequences of complex uncertain variables associated with multiplier sequences. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. [ABSTRACT FROM AUTHOR]

The conception of single-valued quadripartitioned neutrosophic d-ideal (SVQN-d-I) of single-valued quadripartitioned neutrosophic d-algebra (SVQN-d-A) as an expansion of neutrosophic d-Ideal and neutrosophic d-Algebra has been attempted to be introduced in this article. Additionally, we identify various characteristics of them. Additionally, SVQN-d-I and SVQN-d-A examples have been provided. [ABSTRACT FROM AUTHOR]

By using single-valued pentapartitioned neutrosophic set (briefly SVPN-set), one can express uncertainty events having incomplete, indeterminate, and erroneous information in practical applications. This study's primary goal is to present a multi-attribute decision-making (briefly MADM) algorithm that operates in the SVPN-set environment using the notion of single-valued pentapartitioned neutrosophic harmonic mean (briefly SVPNHM) operator and single-valued pentapartitioned neutrosophic weighted harmonic mean (briefly SVPNWHM) operator. Further, we provide a numerical illustration here like, "Location Selection for Installation of Outdoor Air Purifier" to validate the effectiveness and rationality of the proposed MADM algorithm. [ABSTRACT FROM AUTHOR]

In this article, we introduced the idea of lacunary weak convergence of sequences defined by the class of Orlicz function. Various topological and algebraic properties, such as solidity, symmetry, and monotonicity, have been studied. To validate the failure instances, we gave appropriate examples and detailed discussions. Additionally, we have established some inclusion relationships between these spaces. [ABSTRACT FROM AUTHOR]

Convex functions play an important role in finding the inequalities, those help in finding the solutions of different types of equations and equations involving functions. In this article, we have considered convex functions in a normed linear space. We have established some results on composite convex sets and composite convex functions. We have considered quasi-arithmetic mean, that unifies efficiently all types of power means. On applying the principles of composite convex functions, we have established a Hermite-Hadamard like inequality. The functions considered are composite convex functions with respect to a strictly monotonic continuous composite function. The composite convex functions serve as a comprehensive generalization of composite convex functions. As an application, we have established some inequalities on integrable composite convex functions. The results are deferred mean type inequalities. The results on inequalities can be applied for further investigations as well as for application in finding the solutions in different areas of research. [ABSTRACT FROM AUTHOR]

In this paper we investigate the concept of ℐ {\mathcal{I}} -monotonic convergence of sequences of bi-complex numbers. We also discuss some partial order relations ≼ i 2 {\preccurlyeq_{i_{2}}} and ≼ i id {\preccurlyeq_{i_{\rm id}}} between two bi-complex numbers and ℐ {\mathcal{I}} -convergence, ℐ {\mathcal{I}} -monotonic sequences with respect to different partial order relations, ℐ {\mathcal{I}} -Cauchy sequences, ℐ {\mathcal{I}} -bounded monotonic sequences of bi-complex numbers. The analysis indicates that ℐ {\mathcal{I}} -monotonicity with respect to ≼ i 2 {\preccurlyeq_{i_{2}}} is not comparable with ℐ {\mathcal{I}} -monotonicity with respect to ≼ i id {\preccurlyeq_{i_{\rm id}}} . [ABSTRACT FROM AUTHOR]

The notion of relative uniform convergence of a sequence of functions was introduced and investigated by Moore, followed by E. W. Chittenden in the twentieth century. The concept attracted the researcher at the beginning, of the twenty-first century. Jackson F. H. initiated the concept of the notion of the quantum difference operator. We introduced the quantum difference sequence space m(ɸ, ru,∇p), p ≥ 0 of W.L.C. Sargent type. We examine its various properties such as solidity, convergence-free, completeness, etc. Also, some induction results have been established. [ABSTRACT FROM AUTHOR]

We say that a regular graph G of order n and degree r ≥ 1 (which is not the complete graph) is strongly regular if there exist non-negative integers τ and θ such that |Si ∩ Sj | = τ for any two adjacent vertices i and j, and |Si ∩ Sj | = θ for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let λ1 = r, λ2 and λ3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, λ2 and λ3, respectively. We here describe the parameters n, r, τ and θ for strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 7/2 , 7/3 , 7/4 , 7/5 , 7/6 .

In this research article, we introduce ℐ {\mathcal{I}} -statistically pre-Cauchy sequences of complex uncertain variables in five different aspects of uncertainty, namely: in mean, in measure, in distribution, in almost sure, and in uniformly almost sure. We also explore the connection between ℐ {\mathcal{I}} -statistically pre-Cauchy sequences and ℐ {\mathcal{I}} -statistically convergent sequences using complex uncertain variables. Additionally, we initiate the study of ℐ {\mathcal{I}} -statistically pre-Cauchy sequences of complex uncertain variables through Orlicz functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of I3-convergent,I⋆3-convergent and I3-Cauchy triple sequences in a fuzzy normed linear space. Besides, we establish some basic results related to those notions. Furthermore, we define the concepts of I⋆3-Cauchy sequence in fuzzy normed space and some relations between I3-Cauchy sequence in a fuzzy normed space are shown. [ABSTRACT FROM AUTHOR]

The article reveals the investigation of properties of multiplication operation of neutrosophic fuzzy matrices. We study commutative property, associative property, distributive property of them. We show with suitable example that neutrosophic fuzzy matrices do not obey commutative property with respect to multiplication operation. We prove that neutrosophic fuzzy matrices hold associative property property with respect to multiplication operation. We also prove that neutrosophic fuzzy matrices hold distributive property with respect to multiplication operation over addition. These results are further justified by providing suitable numerical examples. The important aspects of the article is that the investigation of commutative, associative and distributive properties of neutrosophic fuzzy matrices with respect to multiplication operation will fill up the gaps in the existing literature. [ABSTRACT FROM AUTHOR]