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Research Square 2021年

作者： Mahapatra, Tanmoy Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India

The saturation graph is a well-defined topic. But, saturation in a fuzzy graph was defined recently and investigated many properties. In a fuzzy saturation graph, only one saturation is considered for every vertex. In a m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining saturation for mPFG is not easy and needs some new ideas. By considering m saturation for each component out of m components of membership values of a vertex, we defined saturation in mPFG. α-saturation as well as β-saturation in mPFG is introduced here. Many interesting properties of it are also presented. α-vertex count and β-vertex count in mPFG are also studied and the upper bound on some well known mPFG is also found here. Finally, a real-life application using saturation in mPFG is also presented. © 2021, CC BY.

关键词： Graph theory

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Analysis of Road Map Design Based on Multigraph with Picture Fuzzy Information

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International Journal of Applied and Computational mathematics 2020年第3期6卷 1-17页

作者： Das, Sankar Ghorai, Ganesh Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India Department of Mathematics Kharagpur College Kharagpur 721 305 India

In this paper, the picture fuzzy planar graph is defined along with some basic properties of picture fuzzy graph. The notion of picture fuzzy planar graphs is introduced and the terms such as strong (weak) edges, strong (weak) picture fuzzy planar graphs, strength of an edge, degree of planarity, picture fuzzy faces, strong (weak) picture fuzzy faces, picture fuzzy dual graphs and picture fuzzy combinatorial dual graphs are defined. Some theorems on degree of planarity and picture fuzzy combinatorial dual graphs have been established. An application of picture fuzzy planar graph in the design of road maps is given. © 2020, Springer Nature India Private Limited.

关键词： Picture fuzzy combinatorial dual graph Picture fuzzy dual graphs Picture fuzzy graphs Picture fuzzy planar graphs Strong (weak) picture fuzzy planar graphs

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A novel reduction method for type-2 uncertain normal critical values and its applications on 4D profit transportation problem involving damageable and substitute items

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International Journal of Applied and Computational mathematics 2021年第4期7卷 1-30页

作者： Sahoo, Palash Jana, Dipak Kumar Pramanik, Sutapa Panigrahi, Goutam Department of Mathematics National Institute of Technology Durgapur Durgapur 713209 West Bengal India School of Applied Sciences & Humanities Haldia Institute of Technology Haldia Purba Midnapur 721657 West Bengal India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 West Bengal India

In this paper, we developed and investigated some four-dimensional profit maximization transportation problems considering damageablity and substitutability, where the parameters are of a type-2 normal uncertain variable in nature. Here, unit transportation cost, distances of the paths, fixed charges, rate of breakability, availability, demands, capacities of conveyances, the unit selling price, unit purchasing cost, unit procurement cost are regarded as type-2 normal uncertain variables. Two models are formulated based on two separate criteria of the substitution items. We use a critical value-based reduction method to reduce type-2 normal uncertain variables into type-1 normal uncertain variables and then apply some properties of uncertainty theory to convert the profit transportation parameters into deterministic form. The two deterministic models are solved using the optimization software named LINGO -18.0. A real-life numerical example and optimal results are presented here to show the application of the proposed model and the proposed reduction method. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Critical value Four dimensional profit transportation problem Reduction method Type-2 normal uncertain variables

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Optimal Control of Dengue-Chikungunya Co-infection: A Mathematical Study 4th

Optimal Control of Dengue-Chikungunya Co-infection: A Mathem...

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4th IFIP TC 12 International Conference on Intelligence Science, ICIS 2020

作者： De, Anupam Maity, Kalipada Panigrahi, Goutam Maiti, Manoranjan Department of Applied Sciences Haldia Institute of Technology Haldia West Bengal India Department of Mathematics Mugberia Gangadhar Mahavidyalaya Bhupatinagar West Bengal India Department of Mathematics National Institute of Technology Durgapur Durgapur West Bengal India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore West Bengal India

ISBN: (纸本)9783030748258

In the present work, we developed a mathematical model for dengue-Chikungunya co-infection to analyze the disease transmission dynamics and interrelationship. We considered the essence of time dependent optimal control with the help of Pontryagin’s maximum principle. The result of diverse combinations of control measures is analyzed and shown graphically. © 2021, IFIP International Federation for Information Processing.

关键词： Co-infection Dengue-Chikungunya Optimal control

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Optimum Production through variational principle with the time quadratic demand, fuzzy time period and fuzzy integrand

arXiv

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arXiv 2023年

作者： Roul, J.N. Maity, K. Kar, S. Maiti, M. Patha Bhavana Visva-Bharati West Bengal Santiniketan731235 India Department of Mathematics M G Mahavidyalaya Bhupatinagar W.B. 721425 India Department of Mathematics National Institute of Technology W.B. Durgapur713209 India Department of Applied Mathematics with Oceanology Computer Programming Vidyasagar University W.B. Midnapore711201 India

Here a real life optimal control problem under fuzzy time period using variational principle is formulated and Solved. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to durability and wear-tear cost. The holding cost is assumed to be non-linear, dependent on time. The profit function which consists of revenue, production cost and holding cost is formulated as a Fuzzy-Final Time and Fixed State System optimal control problem with fuzzy time period. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total profit is maximum. The non-linear optimization technique-Generalised Reduced Gradient Method (LINGO 11.0) is used. The optimum results are illustrated both numerically and *** Codes 49XX Copyright © 2023, The Authors. All rights reserved.

关键词： Profitability

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Evaluating carbon cap and trade policy effects on a multi-period bi-objective closed-loop supply chain in retail management under mixed uncertainty: Towards greener horizons

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Expert Systems with Applications 2024年 250卷

作者： Bhunia, Satyajit Das, Soumen Kumar Jablonsky, Josef Roy, Sankar Kumar Department of Pure and Applied Science Midnapore City College Kuturia West Bengal Bhadutala721129 India Department of Industrial Management National Taiwan University of Science and Technology Taipei Taiwan Department of Econometrics Faculty of Informatics and Statistics Prague University of Economics and Business Praha 3 Prague Czech Republic Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India

In response to the growing imperative of addressing environmental concerns and aligning with governmental regulations in supply chain management, this study navigates the optimization landscape of closed-loop supply chains through the lens of carbon cap and trade policy. The optimization model aims to account for the impact of consumer demands, distribution networks, and retail operations on the overall closed-loop supply chain dynamics. The innovative approach introduces an optimization model designed to grapple with the challenges posed by imprecise information within an intuitionistic type-2 fuzzy framework. The bi-objective mixed-integer model integrates pivotal objectives, including carbon emissions reduction, total cost minimization, and trade policy compliance. For a nuanced comprehension of the proposed model, we present three numerical examples, offering clarity on its complexities. Following this, a sensitivity analysis visually depicts the impact of fluctuations in demand and capacity on the defined objective functions. Furthermore, these conclusions unveil promising avenues for future research and exploration within the ambit of this study. © 2024 Elsevier Ltd

关键词： Multiobjective optimization

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Correction to: Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment

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Artificial Intelligence Review 2023年第12期56卷 15567-15567页

作者： Ghorai, Ganesh Poulik, Soumitra Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India

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Stability Analysis of Imprecise Prey-Predator Model 4th

Stability Analysis of Imprecise Prey-Predator Model

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4th IFIP TC 12 International Conference on Intelligence Science, ICIS 2020

作者： De, Anupam Khatua, Debnarayan Maity, Kalipada Panigrahi, Goutam Maiti, Manoranjan Department of Applied Sciences Haldia Institute of Technology Haldia West Bengal India Department of Basic Science and Humanities Global Institute of Science and Technology Haldia West Bengal India Department of Mathematics Mugberia Gangadhar Mahavidyalaya Contai West Bengal India Department of Mathematics National Institute of Technology Durgapur Durgapur West Bengal India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore West Bengal India

ISBN: (纸本)9783030748258

Since the last few decades, the prey-predator system delivers attractive mathematical models to analyse the dynamics of prey-predator interaction. Due to the lack of precise information about the natural parameters, a significant number of research works have been carried out to take care of the impreciseness of the natural parameters in the prey-predator models. Due to direct impact of the imprecise parameters on the variables, the variables also become imprecise. In this paper, we developed an imprecise prey-predator model considering both prey and predator population as imprecise variables. Also, we have assumed the parameters of the prey-predator system as imprecise. The imprecise prey-predator model is converted to an equivalent crisp model using "e" and "g" operator method. The condition for local stability for the deterministic system is obtained mathematically by analysing the eigenvalues of the characteristic equation. Furthermore, numerical simulations are presented in tabular and graphical form to validate the theoretical results. © 2021, IFIP International Federation for Information Processing.

关键词： Eigenvalues and eigenfunctions

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Fixed-Charge Solid Transportation Problem with Budget Constraints Based on Carbon Emission in Neutrosophic Environment

Research Square

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Research Square 2021年

作者： Ghosh, Shyamali Roy, Sankar Kumar Verdegay, Jose Luis Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India Department of Computer Science and Artificial Intelligence University of Granada Granada Spain

This paper is to integrate among solid transportation problem, budget constraints and carbon emission with probable maximum profit. The limits of air pollution and climate variation are solely dependent by exerting CO2 gas and rest greenhouse gases due to myriad transportation system. Henceforth, it is our apt mission to minimize carbon emission for pollution free environment. Again transportation system with single objective is hardly applicable to the situation with more than one criterion. Therefore multi- objective decision making is incorporated for designing real-life transportation problem. Due to time pressure, data limitation, lack of information or measurement errors in practical problems, there exist some hesitations or suspicions. Based on the fact, decision maker considers indeterminacy in the designed problems. To overcome the restriction on occurrence and non-occurrence of fuzzy and intuitionistic fuzzy, neutrosophic set is very important and suitable to accommodate such general structure of problems. Therefore neutrosophic environment with neutrosophic linear programming, fuzzy programming and global criterion method are profiled to search the compromise solution of the multi- objective transportation problem (MOTP). Thereafter, the performance of the considered model is useful by evaluating a numerical example;and then the derived results are compared. Finally sensitivity analysis and conclusions with upcoming works of this research are stated hereafter. © 2021, CC BY.

关键词： Greenhouse gases

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Intuitionistic Fuzzy Dombi Hybrid Decision-Making Method and Their Applications to Enterprise Financial Performance Evaluation

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Mathematical Problems in Engineering 2021年 2021卷

作者： Jana, Chiranjibe Muhiuddin, G. Pal, Madhumangal Al-Kadi, D. Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India Department of Mathematics University of Tabuk Tabuk71491 Saudi Arabia Department of Mathematics and Statistic College of Science Taif University P.O. Box 11099 Taif21944 Saudi Arabia

In the era of the knowledge-based economy, the active branch of information technology plays a crucial role. The enterprise administration covers efficient changes, and it has been entered in the age of reasonable management argument. The standard enterprise financial review evaluation centers on the importance of bondholders. The investor takes operational data as an issue and pays surveillance to the study of material attraction and the result. Otherwise, it is not intelligent to adjust in a modern marketplace period. Therefore, enterprise financial directing the interests of shareholders and business policies that are taking into account stakeholders' needs is continually investigated in the future lively competition. In that view, accumulating data is an essential research tool to draw the researchers' recent attention during the knowledge investigation. In this research, multiple attribute decision-making (MADM) approach has been proposed for the enterprise financial performance evaluation. To this view, financial performance evaluation has been done with intuitionistic fuzzy arguments. We apply new Dombi hybrid operators such as the intuitionistic fuzzy Dombi hybrid average (IFDHWA) operator and intuitionistic fuzzy Dombi hybrid geometric (IFDHWG) operator. These operators have a good advantage of adaptability in the working parameter. Finally, a realistic instance for enterprise financial performance is reported following comment on the benefit or utility of the recommended output. © 2021 Chiranjibe Jana et al.

关键词： Competition

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