Kandasamy Ganesan

The work addresses the Fully Fuzzy Linear Fractional Programming Problem (FFLFPP) where the objective functions and the constraints are expressed by fuzzy parameters in the form of Triangular Fuzzy Numbers (TFNs) in such a way that the defuzzification to crisp values is not necessary. A hybrid computational framework is proposed to cope with the inherent uncertainty and nonlinearity. The $\alpha$-cut representation is used to convert the fuzzy coefficients to the corresponding parametric forms, while the structural consistency of the original model is maintained. This transformation enables us to convert the FFLFPP into an equivalent Fully Fuzzy Linear Programming (FFLP) model. The obtained model is solved using the LU decomposition method. Also, a theorem for the parametric LU factorization of TFN's is established, revealing the existence conditions and the general form of the solutions. Numerical examples from real life applications demonstrate the efficiency and practical applicability of the proposed approach.

This research presents a fractional-order formulation and mathematical analysis of the Rössler chaotic attractor. By utilizing the Nabla discrete Atangana–Baleanu fractional difference derivative in the Caputo sense, the classical integer-order attractor is extended into the fractional domain. The existence and uniqueness of solutions for the resulting fractional system are established via the fixed-point theorem, thereby ensuring that the recommended attractor is well-posed. Furthermore, the Ulam–Hyers stability is investigated within the Nabla discrete Atangana–Baleanu fractional difference derivative in the Caputo sense framework. For numerical investigations, an Euler numerical scheme adapted to the fractional difference derivative is developed and implemented, yielding high-quality phase portraits of a chaotic attractor. The results highlight the effectiveness of fractional-order modeling and numerical methods in capturing the dynamics and stability of the Rössler chaotic system.

This study examines the fully fuzzy multi-objective linear fractional programming problem (FFMOLFPP), whereby both the objective functions and restrictions incorporate fuzzy parameters represented as triangular fuzzy numbers (TFN), without converting them into crisp values. A hybrid solution approach is presented to tackle the intrinsic nonlinearity and uncertainty. Initially, the imprecise numbers are transformed into parametric representations via the y- cut method. A first-order Taylor series expansion is subsequently utilized to linearize each fractional objective function around a fuzzy decision point. The linearized objectives are then consolidated by the weighted sum approach, transforming the multi-objective fuzzy model into a single-objective linear program. Numerical examples validate the strategy and demonstrate the improved accuracy and efficiency of the proposed methodology.

This article introduces the Augmented Fuzzy Lagrange Multiplier Method (AFLM) as an advanced technique for solving fuzzy nonlinear programming problems (FNLPP) without requiring conversion into crisp equivalents. Unlike traditional methods, which may lead to information loss, AFLM directly transforms constrained fuzzy optimization problems into unconstrained ones while preserving the fuzzy characteristics of the data. The proposed method employs novel fuzzy arithmetic operations and ranking techniques tailored to the parametric representation of Triangular Fuzzy Numbers (TFN), enabling precise handling of both equality and inequality constraints. A key contribution of this work is the development of a convergence theorem and a supporting lemma, ensuring the theoretical soundness of AFLM. The effectiveness of the approach is demonstrated through numerical comparisons, highlighting its ability to achieve more accurate and interpretable solutions than existing methods. The results underscore AFLMs significance as a powerful tool for addressing optimization problems in uncertain environments, making it a valuable asset for decision-makers in fuzzy nonlinear programming problems.

Fuzzy differential equations (FDEs) are used to represent dynamical systems under uncertain environments. Finding solutions for fuzzy differential equations (FDEs) is highly challenging. This work employs the neutrosophic version of the Sumudu transform method to determine the solution to fuzzy differential equations (FDEs) that incorporate Neutrosophic Numbers (NNs). By utilising a novel fuzzy arithmetic operations on the parametric representations of NNs, significant theorems are established to demonstrate the characteristics of Neutrosophic Sumudu Transform (NST). The proposed NST approach is efficient in approximating the solutions of FDEs without converting them into their crisp equivalent forms. An illustrative numerical example is provided to demonstrate the efficacy of the proposed methodology.

In this paper, we formulate a multi-compartmental mathematical model for humans and mosquitoes. We construct the system of differential equations for an SEITVR for the human compartment and an SEI for the mosquito compartment. We investigate the outbreak of malaria and its effect on the Central African Republic. The analysis of the compartmental model is carried out using stability analysis and Routh Hurwitz Criterion technique is used to indicate the major impact of the model and to improve the model through minor modifications in the transformation of disease in the population. Our model exhibits two equilibrium points, disease free equilibrium points and endemic equilibrium points. The next generation matrix is used to determine the basic reproduction number R ₀. A new compartmental model was framed and estimated the malaria spread after 2023 in the Central African Republic, which is the novelty of this research. Our main motivation is to make the Central African Republic a malaria free country. A Numerical example are provided to validate our results for both the disease free state and endemic state of each model. We believe that this investigation will be more effective in reducing malaria infection and stop spreading.

In this article, we investigate fuzzy interior penalty function method for solving fuzzy nonlinear programming problems (FNLPP) based on a new fuzzy arith-metic, unconstrained optimization, and fuzzy ranking on the parametric form of triangular fuzzy numbers (TFN). The main objective of this paper is to solve constrained fuzzy nonlinear programming problems using interior penalty func-tions (IPF) by converting it into unconstrained optimization problems. We prove an important lemma and a convergence theorem for the interior penalty functions method. Interior penalty function techniques favor sites near the boundary of the feasible region in the interior. We present a numerical example of the suggested method and compare the results to those produced by existing methods.

American scientific publishing group

Modelling several real-world issues in the fuzzy world extensively uses ordinary differential equations. In this paper, a mechanical vibration system with the given mass, spring constant, damping and external force is modelled as a second-order ordinary differential equation. Due to measurement errors, the initial displacement of the string is approximate and assumed to be a fuzzy number. A fuzzy version of the Sumudu transform procedure is used to figure out this vibrating spring-mass system with fuzzy initial displacement. The output is displayed as a table at various computational stages. The consequences are visibly presented diagrammatically for different values of r and t. There is a good agreement between the computed results and the analytical solution.

Finding the simplest form of a set of quantities is an important aspect of any branch of Mathematics. Of course, the simplest form or the canonical form as we often call it in mathematics, must possess all the important characteristics of the set of quantities. A real square matrix satisfying certain conditions can be brought to diagonal form which is its simplest form such that the diagonal form retains the eigenvalues, determinants, trace, rank, nullity,.. of the original matrix. Many computations with matrices become easier if one can diagonalize the matrices. In this article, we suggest an approach for diagonalizing interval matrices employing a novel methodology called the pairing technique, which will make it simpler and more effective to classify and investigate interval matrices. This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. We also discuss two real world applications on planar systems and linear discrete dynamical systems.