An intuitionistic fuzzy approach for prey–predator harvesting system with toxicity and time delay M. Mukherjee, D. Pal, S.K. Mahato Decision Analytics Journal, 2024 This study presents an intuitionistic fuzzy prey-predator model with time delay, where several toxic substances from external sources contaminate the prey and predator species. The system consists of one prey and one predator, with the logistic growth of prey species and predation terms proportional to prey density. This system incorporates Holling type-II functional response and introduces a time delay in harvesting prey species over a precise size or age. The primary focus of this work is to investigate the impact of age or size-selective delay on the system’s stability within the intuitionistic fuzzy environment. The model employs triangular intuitionistic fuzzy numbers to account for imprecise biological parameters, and it is converted into an intuitionistic fuzzy model using the Hukuhara derivative. The fuzziness of the model is then resolved using Yager’s Ranking method. Without delay, the paper delves into the system’s dynamics, examining local and global stability and bionomic considerations. Numerical simulations are performed using MATLAB to validate the theoretical findings.
An intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model Ashish Acharya, Sanjoy Mahato, Nikhilesh Sil, Animesh Mahata, Supriya Mukherjee, Sanat Kumar Mahato, Banamali Roy Healthcare Analytics, 2024 Intuitionistic fuzzy sets cannot consider the degree of indeterminacy (i.e., the degree of hesitation). This study presents an intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model. We examine the proposed model by assuming generalized trapezoidal intuitionistic fuzzy numbers for the initial condition. Feasible equilibrium points, along with their stability criteria, are evaluated. We describe the characteristics of intuitionistic fuzzy solutions and clarify the difference between strong and weak intuitionistic fuzzy solutions. Numerical simulations are performed in MATLAB to validate the model results.
A stochastic epidemic model with Crowley–Martin incidence rate and Holling type III treatment Prasenjit Mahato, Sanat Kumar Mahato, Subhashis Das Decision Analytics Journal, 2024 In this work, considering the inevitable effects of environmental perturbation on disease transmission, we investigate a stochastic epidemic model with Crowley–Martin incidence rate and Holling type III treatment. Deterministic model and stochastic model are two parts in model calibration. To analyse the dynamic properties of the stochastic model, we firstly verify that there is unique positive global solution. We establish the sufficient conditions for disease extinction. The sufficient condition for disease persistence is also given. The basic reproduction number (R∗) of the deterministic system is calculated with the help of next generation matrix method. The disease will extinct in long run if the basic reproduction number R∗<1. When R∗>1, the disease will persist. We illustrate the path of the deterministic epidemic model and stochastic model using the Euler–Maruyama method to investigate numerically. The population trajectories of the stochastic model for different noise intensities are presented graphically. Our findings show the importance of considering the influence of stochasticity on the spread of epidemics, particularly in the manifestation of complex incidence mechanism and stochastic environment factors. The stochastic threshold reveals that ordinary differential equation models and white noise models underestimate the severity of disease outbreak.
COVID-19 Outbreak with Fuzzy Uncertainties: A Mathematical Perspective Prasenjit Mahato, Sanat Kumar Mahato, Subhashis Das Journal of Computational and Cognitive Engineering, 2024 In this article, we design a mathematical SEQAIMR (susceptible, exposed, quarantined, asymptomatic, symptomatic, isolated, recovered) epidemic model and investigate the nature of the system. We transform the crisp model into the fuzzy model. All the biological parameters are treated as triangular fuzzy numbers (TFNs). With the help of utility function method, the fuzzy model is defuzzified. We use the MATLAB codes to solve the system of equations and to predict different situations under different values of the control parameters. Lastly, optimal control for COVID-19 disease is explained. Received: 30 April 2022 | Revised: 4 July 2022 | Accepted: 13 July 2022 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement Data sharing is not applicable to this article as no new data were created or analyzed in this study.
Enchanting dynamics: Juvenile and adult predators with prey model in an intuitionistic fuzzy environment Madhurima Mukherjee, Debkumar Pal, Sanat Kumar Mahato, Nabaranjan Bhattacharyee International Journal of Biomathematics, 2024 This study represents an interaction model including juvenile and adult predators along with prey, involving key characteristics like the inability of juvenile predators to reproduce, the impact of adult predators on juvenile growth rates and the transformation of some juveniles to adulthood. Furthermore, it is supposed that adult predators intake prey for sustenance, and the logistic growth of prey is assumed in the non-appearance of adult predators. Intra-species competition among adult predators, together with predation of juveniles and chasing, is conveyed. To tackle the imprecise biological parameters, most parametric values are considered as triangular intuitionistic fuzzy numbers. The model is further processed into an intuitionistic fuzzy model using the Hukuhara derivative and Yager’s ranking method is implemented to make the model crispified. Non-negativity and boundedness of the model are explored, after that, an investigation of possible equilibrium points is discussed. Local and global stability analyses close to these points are supervised. The study accentuates the significant influence of uncertain model parameters on the solution. Especially, uncertain estimates of intra-species competition among adult predators remarkably regulate the model’s stability. Extended uncertainty in intra-species competition for prey, although, is discovered to stabilize the system. In addition, increased consumption of juvenile predators by adult predators is observed to provide the system’s instability.
Analysis of Prey-Predator Scheme in Conjunction with Help and Gestation Delay M. Mukherjee, D. Pal, S. K. Mahato, Ebenezer Bonyah, Ali Akbar Shaikh Journal of Mathematics, 2024 This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.
Mass diffusion with chemical reaction in boundary layer flow due to an exponentially expanding sheet with variable wall concentration Acta Technica CSAV Ceskoslovensk Akademie Ved, 2018
Interval Quadratic Programming Problem with Interval-Valued Decision Variables J Karmakar, S Karmakar, SK Mahato Decision Making Under Uncertainty Via Optimization, Modelling, and Analysis … , 2025 2025
Interval linear programming problem with interval valued decision variables J Karmakar, S Karmakar, SK Mahato OPSEARCH, 1-28 , 2025 2025
Analysis of an imprecise fractional-order eco-epidemiological model with various forms of prey refuges and predator harvesting S Paul, S Mahato, A Mahata, SK Mahato, S Mukherjee, B Roy Brazilian Journal of Physics 55 (1), 12 , 2025 2025 Citations: 10
Exact solutions for 2D boundary layer flow of two types of viscoelastic fluids and heat transfer on a permeable shrinking sheet with thermal radiation and variable surface … A Banerjee, K Bhattacharyya, SK Mahato, AK Verma, AK Gautam, ... Waves in Random and Complex Media 35 (1), 527-552 , 2025 2025 Citations: 3
Enchanting Dynamics: Juvenile and Adult Predators with Prey model in an Intuitionistic Fuzzy Environment M Mukherjee, D Pal, SK Mahato, N Bhattacharyee International Journal of Biomathematics , 2024 2024
An intuitionistic fuzzy approach for prey–predator harvesting system with toxicity and time delay M Mukherjee, D Pal, SK Mahato Decision Analytics Journal 11, 100476 , 2024 2024 Citations: 1
An intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model A Acharya, S Mahato, N Sil, A Mahata, S Mukherjee, SK Mahato, B Roy Healthcare analytics 5, 100294 , 2024 2024 Citations: 10
A stochastic epidemic model with Crowley–Martin incidence rate and Holling type III treatment P Mahato, SK Mahato, S Das Decision Analytics Journal 10, 100391 , 2024 2024 Citations: 6
Neutrosophic trade-credit EOQ model for deteriorating items considering expiration date of the items using different variants of particle swarm optimizations P Supakar, N Kumar, SK Mahato, P Pal International Journal of System Assurance Engineering and Management 15 (3 … , 2024 2024 Citations: 7
Application of artificial bee colony algorithm on a green production inventory problem with preservation for deteriorating items in neutrosophic fuzzy environment P Supakar, AK Manna, SK Mahato, AK Bhunia International Journal of System Assurance Engineering and Management 15 (2 … , 2024 2024 Citations: 25
Analysis of Prey‐Predator Scheme in Conjunction with Help and Gestation Delay M Mukherjee, D Pal, SK Mahato, E Bonyah, AA Shaikh Journal of Mathematics 2024 (1), 2708546 , 2024 2024 Citations: 6
COVID-19 outbreak with fuzzy uncertainties: A mathematical perspective P Mahato, SK Mahato, S Das Journal of Computational and Cognitive Engineering 3 (1), 43-57 , 2024 2024 Citations: 4
A comprehensive study of picture fuzzy planar graphs with real-world applications B Bera, S Amanathulla, SK Mahato Journal of uncertain Systems 16 (04), 2350009 , 2023 2023 Citations: 30
Insight of boundary layer structure with heat transfer through a diverging porous channel in Darcy-Forchheimer porous material with suction/injection: A study of separation control A Banerjee, SK Mahato, K Bhattacharyya, S Rajput, AK Verma, ... Journal of Thermal Engineering 9 (6), 1419-1427 , 2023 2023 Citations: 1
Study of fuzzy fractional caputo order approach to diabetes model S Paul, A Mahata, S Mukherjee, SK Mahato, M Salimi, B Roy Fuzzy optimization, decision-making and operations research: theory and … , 2023 2023 Citations: 6
Analysis of prey-predator optimal control harvesting model in fuzzy uncertain environment D Pal, SK Mahato, M Mukherjee Discontinuity, Nonlinearity, and Complexity 12 (03), 655-671 , 2023 2023 Citations: 6
Fishery type based prey-predator optimal harvesting model under intuitionistic fuzzy environment M Mukherjee, D Pal, SK Mahato Journal of Environmental Accounting and Management 11 (03), 307-327 , 2023 2023 Citations: 6
A prey-refuge harvesting model using intuitionistic fuzzy sets A Acharya, A Mahata, N Sil, S Mahato, S Mukherjee, SK Mahato, B Roy Decision Analytics Journal 8, 100308 , 2023 2023 Citations: 18
Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty M Mukherjee, D Pal, SK Mahato, E Bonyah Scientific African 21, e01837 , 2023 2023 Citations: 10
Stochastic permanence and extinction of an epidemic model with saturated treatment P Mahato, S DAS, SK MAHATO Journal of Biological Systems 31 (02), 691-716 , 2023 2023 Citations: 2
MOST CITED SCHOLAR PUBLICATIONS
Interval-arithmetic-oriented interval computing technique for global optimization SK Mahato, AK Bhunia Applied Mathematics Research Express 2006, 69642 , 2006 2006 Citations: 77
Applications of new hybrid algorithm based on advanced cuckoo search and adaptive Gaussian quantum behaved particle swarm optimization in solving ordinary differential equations N Kumar, AA Shaikh, SK Mahato, AK Bhunia Expert Systems with Applications 172, 114646 , 2021 2021 Citations: 68
Interval oriented multi-section techniques for global optimization S Karmakar, SK Mahato, AK Bhunia Journal of computational and Applied Mathematics 224 (2), 476-491 , 2009 2009 Citations: 57
A new QPSO based hybrid algorithm for constrained optimization problems via tournamenting process: N. Kumar et al. N Kumar, SK Mahato, AK Bhunia Soft Computing 24 (15), 11365-11379 , 2020 2020 Citations: 54
A deteriorating inventory model with displayed stock-level-dependent demand and partially backlogged shortages with all unit discount facilities via particle swarm optimisation AK Bhunia, SK Mahato, AA Shaikh, CK Jaggi International Journal of Systems Science: Operations & Logistics 1 (3), 164-180 , 2014 2014 Citations: 46
Divergent channel flow of Casson fluid and heat transfer with suction/blowing and viscous dissipation: existence of boundary layer A Banerjee, SK Mahato, K Bhattacharyya, AJ Chamkha Partial Differential Equations in Applied Mathematics 4, 100172 , 2021 2021 Citations: 39
A comprehensive study of picture fuzzy planar graphs with real-world applications B Bera, S Amanathulla, SK Mahato Journal of uncertain Systems 16 (04), 2350009 , 2023 2023 Citations: 30
An EPQ model with time proportion deterioration and ramp type demand under different payment schemes with fuzzy uncertainties P Supakar, SK Mahato International Journal of Systems Science: Operations & Logistics 9 (1), 96-110 , 2022 2022 Citations: 29
Design of an efficient hybridized CS-PSO algorithm and its applications for solving constrained and bound constrained structural engineering design problems N Kumar, SK Mahato, AK Bhunia Results in Control and Optimization 5, 100064 , 2021 2021 Citations: 29
Fuzzy reliability redundancy optimisation with signed distance method for defuzzification using genetic algorithm SK Mahato, N Bhattacharyee, R Pramanik International Journal of Operational Research 37 (3), 307-323 , 2020 2020 Citations: 29
Application of artificial bee colony algorithm on a green production inventory problem with preservation for deteriorating items in neutrosophic fuzzy environment P Supakar, AK Manna, SK Mahato, AK Bhunia International Journal of System Assurance Engineering and Management 15 (2 … , 2024 2024 Citations: 25
Disease control prey–predator model incorporating prey refuge under fuzzy uncertainty S Das, P Mahato, SK Mahato Modeling Earth Systems and Environment 7 (4), 2149-2166 , 2021 2021 Citations: 25
Reliability-redundancy Optimization Problem with IntervalValued Reliabilities of Components via Genetic Algorithm KM Sanat, L Sahoo, AK Bhunia Journal of Information and Computing Science 7 (4), 284-295 , 2012 2012 Citations: 25
A prey predator model in case of disease transmission via pest in uncertain environment S Das, P Mahato, SK Mahato Differential Equations and Dynamical Systems 31 (2), 457-483 , 2023 2023 Citations: 20
An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness P Mahato, S Das, SK Mahato Modeling earth systems and environment 8 (3), 2863-2887 , 2022 2022 Citations: 20
A new QPSO based hybrid algorithm for bound-constrained optimisation problem and its application in engineering design problems N Kumar, MS Rahman, A Duary, SK Mahato, AK Bhunia International Journal of Computing Science and Mathematics 12 (4), 385-412 , 2020 2020 Citations: 20
A prey-refuge harvesting model using intuitionistic fuzzy sets A Acharya, A Mahata, N Sil, S Mahato, S Mukherjee, SK Mahato, B Roy Decision Analytics Journal 8, 100308 , 2023 2023 Citations: 18
A mathematical model of a prey-predator type fishery in the presence of toxicity with fuzzy optimal harvesting D Pal, GS Mahapatra, SK Mahato, GP Samanta Journal of applied mathematics & informatics 38 (1_2), 13-36 , 2020 2020 Citations: 17
Optimization of system reliability for multi-level RAPs in intuitionistic fuzzy atmosphere using genetic algorithm R Paramanik, SK Mahato, N Kumar, N Bhattacharyee, RK Gupta Results in Control and Optimization 9, 100175 , 2022 2022 Citations: 16
Optimal redundancy allocation for the problem with chance constraints in fuzzy and intuitionistic fuzzy environments using soft computing technique N Bhattacharyee, R Paramanik, SK Mahato Annals of Optimization Theory and Practice 3 (2), 25-47 , 2020 2020 Citations: 16
