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作者： Pramanik, Tarasankar Pal, Madhumangal Mondal, Sukumar Samanta, Sovan Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India Department of Mathematics Raja N. L. Khan Women's College Midnapore India Department of Mathematics Tamralipta Mahavidyalaya Tamluk India

In this paper, bipolar fuzzy planar graph is defined and studied several properties. The bipolar fuzzy planar graph is defined in a very interesting way. The parameter "degree of planarity" measures the planarity of a bipolar fuzzy graph. The other relevant terms such as strong edges, bipolar fuzzy faces, strong bipolar fuzzy faces are defined here. A very close association of bipolar fuzzy planar graph is bipolar fuzzy dual graph. This is also defined and several properties of it are studied. Bipolar fuzzy planar graph and bipolar fuzzy dual graph have many applications in different fields including design of social network, design of subway tunnel or routes, gas or oil pipelines, image segmentation, etc. © 2018 - IOS Press and the authors. All rights reserved.

关键词： Image segmentation

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Dynamics of a predator-prey model with nonlinear incidence rate, Crowley-Martin type functional response and disease in prey population

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Ecological Genetics and Genomics 2019年 10卷

作者： Mortoja, Sk Golam Panja, Prabir Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 WB India Department of Applied Science Haldia Institute of Technology Haldia Purba Midnapore 721657 WB India

In this paper, a delayed predator-prey model has been developed. Here, on the basis of infectious disease, the prey population has been divided into two sub-populations such as (i) susceptible prey and (ii) infected prey population. It is also assumed that a predator may consume both susceptible prey as well as infected prey. Also here, the Crowley-Martin type functional form has been taken to consume the prey (both susceptible and infected) population by the predator. It also considers two types of time delays in this model, (i) one is disease transmission delay when susceptible prey moves to infected prey stage and (ii) other is predator maturation delay. As the predator consumes both susceptible and infected prey, so we have incorporated the fact in this model that disease in the prey species also effect on predator population growth. Here, positivity and boundedness of solutions of our proposed model have been discussed. Then calculating different equilibrium points, the stability of the system have been discussed around those. In this paper, the Hopf bifurcation analysis has been done for non-delayed system with respect to the crowding coefficient. Finally, some numerical simulations have been presented to validate our theoretical findings. © 2018 Elsevier Inc.

关键词： Crowley-Martin functional response Hopf bifurcation Nonlinear incidence rate Predator-prey model Stability analysis Time delay

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Dynamics of a predator-prey model with stage-structure on both species and anti-predator behavior

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Informatics in Medicine Unlocked 2018年 10卷 50-57页

作者： Mortoja, Sk Golam Panja, Prabir Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 W.B. India Department of Applied Science Haldia Institute of Technology Purba Midnapore Haldia 721657 W.B. India

In this paper, we have formulated and studied a stage-structure predator-prey model. Here, we consider stage-structure on both prey as well as predator population which means that the prey population is divided into two sub populations such as juvenile prey and adult prey, on the other hand, the predator population is also divided into two sub populations such as juvenile predator and adult predator. It is assumed that only adult predator have the ability to predation and they consume both juvenile prey as well as adult prey. Here, it is also considered that the growth rate of juvenile prey depends upon the adult prey population i.e., the juvenile prey has no reproduction capability. Also, Holling II and Holling IV response function have been used for the consumption of juvenile prey and adult prey by adult predator respectively. It is also considered two types of factors such as anti-predator behavior and group defense to formulate our proposed model. Mathematically, we have analyzed the positivity and boundedness of solutions, existence of equilibria, stability of the proposed system around these equilibrium points and Hopf bifurcation of interior equilibrium point. Finally, some numerical simulations have been presented to validate our theoretical results. © 2017

关键词： Anti-predator behavior Group defense Holling IV response function Prey-predator model Stability analysis Stage-structure

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Application of Interval Type-2 Fuzzy Logic to polypropylene business policy in a petrochemical plant in India

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Journal of the Saudi Society of Agricultural Sciences 2018年第1期17卷 24-42页

作者： Jana, Dipak Kumar Castillo, Oscar Pramanik, Sutapa Maiti, Manoranjan Department of Engineering Science Haldia Institute of Technology Haldia Purba Midnapur 721 657 West Bengal India Tijuana Institute of Technology Tijuana Mexico Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 West Bengal India

This paper presents a new approach to predict the quality of polypropylene in petrochemical plants. The proposed approach constructs four different models, based on a large number of data collected from a renowned petrochemical plant in India and uses it to predict the polypropylene quality. The quality of polypropylene depends on the indices such as melt flow index and the xylene solubility of the product and the parameters controlling these two indices are hydrogen flow, donor flow, pressure and temperature of polymerization reactors. Mamdani Interval Type-2 Fuzzy Logic inference systems are formed for first time. The model outcomes are compared with the collected plant data and a sequence of sensitivity analysis elects the most suitable model from them. Some sensitivity analyses are provided using Fuzzy C-Means Clustering to the models. © 2015 The Authors

关键词： Fuzzy C-Means Clustering Fuzzy inference system Interval Type-2 Fuzzy Logic Polypropylene Product quality

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Product of interval-valued fuzzy graphs and degree

Product of interval-valued fuzzy graphs and degree

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作者： Rashmanlou, Hossein Pal, Madhumangal Borzooei, Rajab Ali Mofidnakhaei, F. Sarkar, Biswajit Department of Computer Science University College of Adib Sari Iran Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India Department of Mathematics Shahid Beheshti University Tehran Iran Department of Physics Sari Branch Islamic Azad University Sari Iran Department of Industrial and Management Engineering Hanyang University Erica Campus Ansan Korea Republic of

Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they have many applications in networks. In this paper, at first we define three new operations on interval-valued fuzzy graphs namely strong product, tensor product and lexicographic product. Likewise, we study about the degree of a vertex in interval-valued fuzzy graphs which are obtained from two given interval-valued fuzzy graphs using the operations Cartesian product, composition, tensor and strong product of two interval-valued fuzzy graphs. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large interval-valued fuzzy graph as a combination of small, interval-valued fuzzy graphs and to derive its properties from those of the smaller ones. © 2018 - IOS Press and the authors. All rights reserved.

关键词： Image segmentation

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Modeling and Analysis of an Imprecise Epidemic System with Optimal Treatment and Vaccination Control

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Biophysical Reviews and Letters 2018年第2期13卷 37-60页

作者： Anjana Das M. Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721101 West Bengal India Department of Mathematics Sura Mahamaya Balika Vidyalaya Panskura 721152 West Bengal India

In this paper, we propose and analyze a Susceptible-Vaccinated-Exposed-Infected-Recovered (SVEIR) type infectious disease model with imprecise parameters. Introducing the interval numbers in functional form, the SVEIR model is proposed and formulated. The existence of possible equilibrium points with their feasibility criteria and an explicit value of basic reproduction number is obtained. The asymptotic stability of the system at different equilibrium points are also discussed. Next by considering treatment and vaccination as two control parameters, an optimal control problem is formulated and solved. Finally, some computer simulation works are given in support of our analytical results.

关键词： Basic reproduction number imprecise parameter optimal control transcritical bifurcation

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Certain Types of Product Bipolar Fuzzy Graphs

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International Journal of Applied and Computational mathematics 2017年第2期3卷 605-619页

作者： Ghorai, Ganesh Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

Recently, bipolar fuzzy graph is a vastly growing research area as it is the generalization of the fuzzy graphs. In this paper, at first the concepts of regular and totally regular product bipolar fuzzy graphs is introduced. Then necessary and sufficient conditions are established under which regular and totally regular product bipolar fuzzy graph becomes equivalent. The notion of product bipolar fuzzy line graph is introduced and investigated some of its properties. A necessary and sufficient condition is given for a product bipolar fuzzy graph to be isomorphic to its corresponding product bipolar fuzzy line graph. It is also examined when an isomorphism between two product bipolar fuzzy graphs follows from an isomorphism of their corresponding fuzzy line graphs. © 2015, Springer India Pvt. Ltd.

关键词： Bipolar fuzzy sets Product bipolar fuzzy graphs Product bipolar fuzzy line graphs Regular product bipolar fuzzy graphs Totally regular product bipolar fuzzy graphs

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Novel Concepts of Strongly Edge Irregular m-Polar Fuzzy Graphs

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International Journal of Applied and Computational mathematics 2017年第4期3卷 3321-3332页

作者： Ghorai, Ganesh Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle m-polar fuzzy information by combining the theory of m-polar fuzzy sets with graphs. We introduce the notion of strongly edge irregular and strongly edge totally irregular m-polar fuzzy graphs. Some properties of them are also studied to characterize strongly edge irregular and strongly edge totally irregular m-polar fuzzy graphs. © 2016, Springer India Pvt. Ltd.

关键词： Highly irregular m-polar fuzzy graphs m-Polar fuzzy graphs Strongly edge irregular Strongly edge totally regular

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A hybrid heuristic for restricted 4-dimensional TSP (r-4DTSP) 1st

A hybrid heuristic for restricted 4-dimensional TSP (r-4DTSP...

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1st International Conference on Frontiers in Optimization: Theory and Applications, FOTA 2016

作者： Roy, Arindam Chakraborty, Goutam Khan, Indadul Maity, Samir Maiti, Manoranjan Department of Computer Science Prabhat Kumar College Contai Purba MedinipurW.B721401 India Faculty of Software and Information Science Iwate Prefectural University Takizawa Japan Department of Computer Science Vidyasagar University MedinipurW.B721102 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University MedinipurW.B721102 India

ISBN: (纸本)9789811078132

In this paper, we proposed a hybridized soft computing technique to solve a restricted 4-dimensional TSP (r-4DTSP) where different paths with various numbers of conveyances are available to travel between two cities. Here, some restrictions on paths and conveyances are imposed. The algorithm is a hybridization of genetic algorithm (GA) and swap operator-based particle swarm optimization (PSO). The initial solutions are produced by proposed GA which used as swarm in PSO. The said hybrid algorithm (GA-PSO) is tested against some test functions, and efficiency of the proposed algorithm is established. The r-4DTSPs are considered with crisp costs. The models are illustrated with some numerical data. © 2018, Springer Nature Singapore Pte Ltd.

关键词： Genetic algorithms

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An Imprecise Eco-Epidemic Model with Pesticide in Relevance to Agricultural Pest Control

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Biophysical Reviews and Letters 2018年第3期13卷 109-131页

作者： Anjana Das M. Pal http://***/0000-0003-4462-0490 Department of Mathematics Sura Mahamaya Balika Vidyalaya Panskura 721152 West Bengal India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721101 West Bengal India

In this paper, we have proposed and analyzed an agricultural pest control system. For this purpose, an eco-epidemiological type predator–prey model has been proposed with the consideration of a sound predator population and two classes of pest populations namely susceptible pest and infected pest. Further to consider uncertainty, we modify our model and transform it into a fuzzy system with incorporation of imprecise parameters. The dynamical behavior of the proposed model has been investigated by examining the existence and stability criteria of all feasible equilibria. An optimal control problem is formed by considering the pesticide control as the control parameter and then the problem is solved both theoretically and numerically with the help of some computer simulation works.

关键词： Eco-epidemiology bifurcation global stability optimal control

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