University of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Finding a generalized positive solution equation for a trapezoidal fully fuzzy sylvester matrix167175353910.22098/jhs.2024.15376.1024ENRam MilanSinghInstitute for Excellence in Higher Education, Bhopal, India0000-0001-6269-5248Journal Article20240630The solvability of Sylvester matrix equations is relevant to many issues in control theory and systems theory. Fuzzy numbers should be used to represent at least some of the system’s parameters in many applications instead of crisp ones. The solutions to the fuzzy Sylvester matrix problem are only given with triangular fuzzy numbers in the majority of the earlier literature. Two analytical approaches to the solution of the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation are presented in this study. The Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation is transformed utilising the current arithmetic fuzzy multiplication operations into an analogous system of crisp Sylvester Matrix Equations. We look into the uniqueness and necessary and sufficient circumstances for the existence of the positive fuzzy solutions to the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation. We look into the uniqueness and necessary and sufficient circumstances for the existence of the positive fuzzy solutions to the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation. Furthermore, the equivalency between the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation and the solution to the Sylvester Matrix Equation system is examined. One example problem is solved to demonstrate the suggested methods.https://jhs.uma.ac.ir/article_3539_ae170ec95831737decbfba544c827d43.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Some characterizations of the maximal ZG-regular ideal in a ring176183407510.22098/jhs.2025.17344.1090ENMarziehFarmaniDepartment of Mathematices, Islamic Azad University, Roudehen Branch, Roudehen, Tehran, Iran.Journal Article20250430Let R be an associative ring with identity. A ring R is called ZG-regular( resp. strongly ZG-regular) if, for every a in R, there exist positive integer n and g in G, such that a<sup>ng</sup> ∈a^<sup>ng</sup>Ra^<sup>ng</sup> (resp. a^<sup>ng</sup> ∈a^<sup>(n+1)g</sup>R. In this paper, we shall show that the join of all ZG-regular ideals in an arbitrary ring R is a ZG-regular ideal, and so there exists a unique maximal ZG-regular ideal M = M(R) in R, whose structure we investigate. Furthermore, we establish the necessary and sufficient condition for a ring to be a direct sum of its ideals.https://jhs.uma.ac.ir/article_4075_75a57207586e453520042c40de955d93.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Depth of an ideal on a pair of modules184190419110.22098/jhs.2025.17916.1116ENMortezaLotfi ParsaDepartment of Mathematics, Sayyed Jamaleddin Asadabadi University, Asadabad, IranJournal Article20250726Let R be a commutative Noetherian ring and I an ideal of R. Suppose that S is a Serre subcategory of the category of R-modules which satisfies the condition C<sub>I</sub>. Let $M$ be a ZD-module and N an R-module. As a generalization of the notion of S-depth(I, M), we define the S-depth of I on the pair (N, M) by S-depth(I, N, M):=S-depth(Ann<sub>R</sub>(N/IN), M). We investigate the connections between S-depth(I, N, M), local cohomology modules and Ext functors. In particular, when N is finitely generated, it is shown that S-depth(I, N, M)=inf {i: H<sup>{i}</sup><sub>I</sub>(N, M) ∉ S}=inf{i: Ext<sup>i</sup><sub>R</sub>(N/{IN}, M)∉ S}. Moreover, various formulas are provided that relate this generalized S-depth to other notions of depth in the literature.https://jhs.uma.ac.ir/article_4191_c6e6f5e958ec11a780d53043951d5eb7.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Monophonic domination integrity in fuzzy graphs191207389910.22098/jhs.2025.16407.1064ENSherly SJasminDepartment of Mathematics, Scott Christian College (Autonomous), Tamil Nadu, India,S. ChandraKumarDepartment of Mathematics, Scott Christian College (Autonomous),Tamil Nadu, India.Journal Article20241220Let M be a subset of V (G) and let G : (V, σ, μ) be a fuzzy graph. The monophonic domination integrity (MDI) of G is defined by (MDI) ̃(G)^= min{|M|+m(G−M): M is a monophonic dominating set of G}, where |M|=∑_(u∈M)σ(u)and m(G − M) is the order of the greatest component of G−M. The notion of vulnerability parameter MDI in fuzzy graphs is presented in this work. Further, the MDI for complete fuzzy graph, complete bipartite fuzzy graph, join and Cartesian product of two fuzzy graphs and bounds are also discussed. Also, we present a decision-making problem involving the optimization of bus routes and the strategic placement of bus stations using MDI principles.https://jhs.uma.ac.ir/article_3899_b6087cee9d9b71b09487882a54bf1434.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Total outer-connected dominating sets and total outer-connected domination polynomial of complete bipartite graph K2,n208216419210.22098/jhs.2025.16719.1073ENGracelin GoldyJ VDepartment of Mathematics, Scott Christian College (Autonomous),
Nagercoil - 629 003, Kanyakumari District, Tamilnadu, India.
(Affiliated to Manonmaniam Sundaranar University, Abishekapatti,
Tirunelveli-627 012Lal GipsonKDepartment of Mathematics, Scott Christian College(Autonomous),Nagercoil-629003.Affilliated to Manonmanium Sundaranar University,Abishekapatti,Tirunelveli-627012Journal Article20250205Let G = (V, E) be a simple graph. A set D⊆V (G) is a total outer−connected dominating set of G if D is total dominating, and the induced sub-graph G[V (G) − D] is a connected graph. Let K<sub>2,n</sub> be the complete bipartite graph and D ̃<sub>tc</sub> (K<sub>2,n</sub>,i) denote the family of all total outer-connected dominating sets of K<sub>2,n</sub> with cardinality i. Let d ̃<sub>tc</sub> (K<sub>2,n</sub>,i)=|D ̃<sub>tc</sub> (K<sub>2,n</sub>,i)|. In this paper, we obtain recursive formula for d ̃<sub>tc</sub> (K<sub>2,n</sub>,i). Using this recursive formula, we construct the polynomial, D~<sub>tc</sub> (K<sub>2,n</sub>,x)=∑<sub>i=2</sub><sup>2+n</sup>d ̃<sub>tc</sub> (K<sub>2,n</sub>,i)x<sup>i</sup> which we call total outer−connected domination polynomial of K<sub>2,n</sub> and obtain some properties of this polynomial.https://jhs.uma.ac.ir/article_4192_879255e1aa44db1139f9487335951831.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201On the distance-based indices of Mobius function graph of finite groups217232393610.22098/jhs.2025.16816.1075ENRaniJoseDepartment of Mathematics, St. Dominics College, Kanjirapally, Kottayam, IndiaSUSHAD2Department of Mathematics, Catholicate College, Pathanamthitta - 689645, Kerala, IndiaJournal Article20250217In the domain of mathematical chemistry and graph theory, topological indices have emerged as vital tools for quantifying the structural properties of molecular graphs. Recently, the Mobius function graph of a finite group has earned significant attention due to its connections with algebraic and topological structures. However, determination of the topological indices of these graphs remain largely unexplored. In this paper we compute and investigate the relationships between several distance-based topological indices, including the Mostar index, weighted Mostar index, Szeged index, weighted Szeged index, PI index and weighted PI index, for the Mobius function graphs of finite groups. https://jhs.uma.ac.ir/article_3936_3456c38f2a8531da3c2f05bd72696659.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201The edge Seidel and minimum edge covering Seidel energy of the K1,n and K2,n graphs233241394010.22098/jhs.2025.17132.1084ENAkram SadatBanihashemi DehkordiDepartment of Mathematics, Statistics and Computer Science, Semnan UniversitySaeedMohammadian SemnaniDepartment of Mathematics, Statistics and Computer Science, Semnan UniversityMehdiAlaeiyanSchool of Mathematics, University of Sciences and Technology, P.O. Box: 16846-13114, Tehran, Iran.Journal Article20250407The Seidel energy of a graph is the sum of the absolute values of the eigenvalues of its Seidel matrix. In this paper, we introduce the concepts of edge Seidel energy E(Ls(G)) and edge covering Seidel energy E(Lsec(G)) for the K<sub>1,n</sub> and K<sub>2,n</sub> Graphs, and we have obtained some results.https://jhs.uma.ac.ir/article_3940_d6d17aa92539af5545090c2f22835d18.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Computation of NM-polnomial and topological indices for cycle related graphs242255427510.22098/jhs.2025.17644.1100ENDeepasree SKumar1Acharya Institute of Technology, Bangalore, affiliated to Visvesvaraya Technological University, Belagavi, Karnataka,
India.P SRanjini2Department of Mathematics,Don Bosco Institute Of Technology, Kumbalagudu, Bangaluru-56, Karnataka, India.Harini MR3Department of Mathematics,PES College of Engineering, Mandya, Karnataka, India.LokeshaV4DOS in Mathematics, Vijyanagara Sri Krishnadevaraya University, Ballari-583105, India.Journal Article20250610This paper focuses on the computation of NM-polynomial and several topological indices for cycle related graphs such as Wheel graph, Helm graph and Gear graph. The NM-polynomial is a graph invariant that encodes information about the sub graph structure, which is crucial for understanding the connectivity and combinatorial properties of a graph. We develop formulas and methods for computing the NM-polynomial for specific cycle-related graphs, demonstrating its utility in capturing key graph characteristics.https://jhs.uma.ac.ir/article_4275_19af1e74bd283c039ee9f51542064fce.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201On the distance transitivity of the bipartite Kneser graphs256267427310.22098/jhs.2025.17995.1122ENMeysamZiaeeDepartment of Mathematics, Iranmehr Univertsity, Kordestan, IranJournal Article20250805In this paper, we study a family of graphs related to Johnson graphs, known as bipartite Kneser graphs. Let n and k be integers such that n>k 1≥. We denote by H(n, k) the bipartite Kneser graph, whose vertex set consists of all k-subsets and (n - k)-subsets of the set [n] = {1, 2, ..., n}, where two vertices are adjacent if and only if one is a subset of the other. Mirafzal (S. M. Mirafzal, The automorphism group of the bipartite Kneser graph, Proc. Indian Acad. Sci. (Math. Sci.), (2019) 129 (34), proved that the automorphism group of the bipartite Kneser graph H(n, k) is isomorphic to Sym ([n])×Z<sub>2</sub>. In this paper, we investigate the distance-transitivity and the diameter of the bipartite Kneser graphs. It is known that H(n, k) is distance-transitive precisely when k=1 or n=2k+1. In this work, we provide new structural proofs of these cases directly within the bipartite Kneser framework, and we determine the diameter of H(n, k) for various ranges of n and k.https://jhs.uma.ac.ir/article_4273_2c52936860f226a3156c88e15d99c5d9.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Twain Secure Perfect Dominating Sets and Twain Secure Perfect Domination Polynomials of Cycles268275427410.22098/jhs.2025.16747.1074ENVinishaCDepartment of Mathematics, Scott Christian College (Autonomous), Nagercoil-629 003, Manonmaniam Sunderanar University, India.K. LalGipsonDepartment of Mathematics,Scott Christian College (Autonomous), Nagercoil-629003, Manonmaniam Sunderanar University, India.Journal Article20250207Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of G, if for every vertex in V\S is adjacent to at least one vertex in S. A subset S of V is called a twain secure perfect dominating set of G (TSPD-set) if for every vertex v ∈ V \S is adjacent to exactly one vertex u ∈ S and (S\{u})∪{v} is a dominating set of G. The minimum cardinality of a twain secure perfect dominating set of G is called the twain secure perfect domination number of G and is denoted by γ<sub>tsp</sub>(G).<br />Let D<sub>tsp</sub>(C<sub>n</sub>, i) denote the family of all twain secure perfect dominating sets of C<sub>n</sub> with cardinality i, for γ<sub>tsp</sub>(C<sub>n</sub>)≤ i≤ n. Let d<sub>tsp</sub>(C<sub>n</sub>, i) = |D<sub>tsp</sub>(C<sub>n</sub>, i)|. In this article, we derive a recursive formula for d<sub>tsp</sub>(C<sub>n</sub>, i) and construct D<sub>tsp</sub>(C<sub>n</sub>, i). We<br />consider the polynomial D<sub>tsp</sub>(C<sub>n</sub>, x) = Σ<sup>n</sup> <sub>i=γtsp(Cn)</sub> d<sub>tsp</sub>(C<sub>n</sub>, i)x<sup>i</sup>, which we refer to as the twain secure perfect domination polynomial of cycles using this recursive formula. In this research, we use a recursive technique to generate all twain secure perfect dominating sets of cycles and twain secure perfect domination polynomials of cycles.https://jhs.uma.ac.ir/article_4274_004fa7c35d20f8e31484cfdf497801c0.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Mellin-Sumudu Synergy: A Novel Paradigm for Extending Mittag-Leffler Function276288405610.22098/jhs.2025.16472.1069ENMousmiKulmitra1Department of Mathematics, Govt. Rajmata Vijaya Raje Sindhiya Kanya Mahavidyalaya Kawardha, Dist.- Kabirdham (C.G.), IndiaOmprakashDewanganIndira Gandhi Govt. College Pandaria, Distt.- Kabirdham, Hemchand Yadav Vishwavidyalaya Durg, Chhattisgarh, IndiaJournal Article20241231This study presents an innovative reconfiguration of the Mittag-Leffler function (MLF) by synergistically combining the Mellin transform and the Sumudu transform. Although the MLF plays a significant role in fractional calculus, its complexity has limited its applicability. By utilizing both the Mellin and Sumudu transforms, new integral representations of the MLF are derived, effectively broadening its scope in addressing fractional differential equations. This integrated approach provides a deeper understanding of the MLF’s properties and enables its extension to a wider range of problems in physics, engineering, and mathematics. The effectiveness of the proposed extension is demonstrated through its application to fractional calculus problems, thereby contributing to the advancement of the field and enhancing its ability to model complex real-world phenomena with greater accuracy.https://jhs.uma.ac.ir/article_4056_b6a81573d2d3f5139f8592fd65cf620f.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Advanced studies in pentagonal controlled intuitionistic fuzzy metric spaces with applications289305405510.22098/jhs.2025.16011.1052ENRam MilanSinghInstitute for Excellence in Higher Education, Bhopal, India0000-0001-6269-5248Journal Article20241014This paper introduces Pentagonal Controlled Intuitionistic Fuzzy Metric Spaces (PCIFMS), a novel extension of intuitionistic fuzzy metric spaces that incorporates a pentagonal control function to better handle uncertainty and imprecision. We establish foundational theorems, provide detailed proofs, and explore practical applications in decision-making, image processing, and complex systems analysis. The proposed model offers significant advantages over existing frameworks, particularly in its ability to adapt to multi-dimensional and context-dependent scenarios. This study contributes to the development of fuzzy theory and its applications, providing a robust tool for modeling complex systems under uncertainty.https://jhs.uma.ac.ir/article_4055_141c717ec332dd94cec1e1837b3c757c.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201On generalized Berwald R-quadratic metrics306314393710.22098/jhs.2025.16423.1065ENMohammadMtashar Alzuhairydepartment of mathematics, urmia universityBahmanRezaeiDepartment of mathematics, Urmia University, Urmia , IranAkbarTayebidepartment of mathematics, qom universityJournal Article20241223Every Riemannian metric is R-quadratic, while many Finsler metrics have not this property. A Finsler metric is called R-quadratic if its Riemannian curvature is quadratic in all direction at any points of the underlying manifold. A Finsler metric on a manifold is called a generalized Berwald metric if there exists a covariant derivative such that the parallel translations induced by it preserve the Finsler function. In this paper, we study the class of generalized Berwald (α, β)-manifolds with R-quadratic properties and prove a rigidity result. We show that such manifolds satisfy <strong>S</strong>=0 if and only if <strong>B</strong>=0.https://jhs.uma.ac.ir/article_3937_accd5a7c207d58bbc49a47d460d0d826.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Homotopic embeddings of infinite-dimensional Hilbert Manifolds into Poincaré complexes315326405410.22098/jhs.2025.15968.1048ENJEYANTHIV1Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore, IndiaMADHANV2Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore, India,Journal Article20241008This manuscript explores the Homotopic embedding of infinite-dimensional Hilbert manifolds into Poincaré complexes, emphasizing the preservation of necessary geometric properties such as curvature and Ricci-flatness. The exploration of infinite-dimensional Hilbert manifolds and their embeddings into Poincaré complexes has opened up new pathways in the fields of functional analysis, algebraic topology, and differential geometry. Recent studies emphasize the preservation of geometric features such as curvature and Ricci-flatness, which have greatly enriched the understanding of symplectic geometry and topological properties of manifolds.https://jhs.uma.ac.ir/article_4054_237790d8e0af13b23e27ceda679e1bf9.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201On the distribution generated by Waring-type probability with application to COVID-19 data327340410510.22098/jhs.2025.16442.1068ENDavoodFarbodDepartment of Mathematics, Faculty of Engineering Science, Quchan University of Technology, Quchan, Iran.Journal Article20241226Farbod (2024) introduced a 2-parameter regularly varying discrete distribution generated by Waring-type probability (2-RDWP). In this paper, asymptotic properties of maximum likelihood estimators of the unknown parameters are established for the 2-RDWP model. Some new plots including cumulative distribution function, survival function and hazard rate function are illustrated for the 2-RDWP model. Two real data sets of COVID-19 are applied to show the model's applicability compared to other rival distributions. Based on some statistical criteria we see that the 2-RDWP, for these real data sets, has satisfactory results with respect to rival models. Using an optimization algorithm, maximum likelihood estimations of the unknown parameters are proposed.https://jhs.uma.ac.ir/article_4105_6abe037abea4ccb33cf5a773bfe562fa.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201Stochastic robustness in switched systems: A novel control strategy for random time-iteration driven switching341357386610.22098/jhs.2025.15886.1045ENOmprakashDewanganIndira Gandhi Govt. College Pandaria, Distt.- Kabirdham, Hemchand Yadav Vishwavidyalaya Durg, Chhattisgarh, India.Journal Article20240920This paper addresses the control of a category of continuous-time linear systems that switch between different modes, where the switching signals are driven by random time-iteration. The system under consideration is subject to uncertainties in the system dynamics and observation noise in the output measurements. We propose a robust control strategy that Accounting for the random nature of the switching signals and the system uncertainties. The learning performance is examined using the Lebesgue-p norm, leading to the derivation of a sufficient condition for convergence. The findings demonstrate that the proposed control law effectively addresses the tracking problem in switched systems, Especially when the switching rules are expanded to the time-iteration domain using a stochastic framework, we introduce a groundbreaking control approach that guarantees the system's performance despite uncertainties and noise. Through rigorous theoretical analysis, we prove the effectiveness of our suggested approach in achieving robust control and estimation performance.The results of this research contribute to the advancement of control theories and have potential applications in various fields, including power systems, robotics, and process control.https://jhs.uma.ac.ir/article_3866_a27788e2ef4d23f2741d8450b916153e.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843614220251201An application of fuzzy time series with different universal discourse interval lengths for rice production in India358371389210.22098/jhs.2025.15725.1041ENB.Mohamed HarifPG and Research Department of Mathematics, Rajah Serfoji Government College
(Autonomous), Affiliated to Bharathidasan University, Thanjavur, India-613005.KarthikeyanMResearch Scholars, PG and Research Department of Mathematics,
Rajah Serfoji Government College (Autonomous), Thanjavur-05 Tamilnadu, India.SureshRSRM Institute of Science and Technology, Tiruchirappalli, Tamilnadu, IndiaJournal Article20240826In this paper, we offered a FTS-based tutorial on rice farming in India. The relevant literature is reviewed, which serves as a basis for the main concepts and models based on different forms of FTS forecasts. In an effort to inspire readers to contribute to this field of study, we also highlight the challenges and recent work that aims to fill in some of these knowledge gaps. Finally, time series forecasting is a useful tool for organizing and making decisions. An increasing number of methods, ranging from traditional statistical models to soft computing and artificial intelligence approaches, have been developed to generate increasingly accurate forecasts. PyFTS is an open-source, free Python library created by the Laboratory of Machine Intelligence and Data Science that implements a number of FTS models that have been published in the literature. In order to determine the interval in the fuzzy time series, Chen's method of FTS, comparing numerous values of n (Number of Interval) is used in this paper. We are interested to minimizing the MSE in the forecasting using PyFTS.https://jhs.uma.ac.ir/article_3892_0903bca4a87f420635881f814aea99ba.pdf