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Scheduling Algorithm to Select Optimal Programme Slots in Television Channels: A Graph Theoretic Approach

International Journal of applied and Computational mathematics 2017年第3期3卷 1931-1950页

作者： Pal, Madhumangal Pal, Anita Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India Department of Mathematics National Institute of Technology Durgapur Mahatma Gandhi Avenue Durgapur 713 209 West Bengal India

In this paper, it is shown that all programmes of all television channels can be modelled as an interval graph. The programme slots are taken as the vertices of the graph and if the time duration of two programme slots have non-empty intersection, the corresponding vertices are considered to be connected by an edge. The number of viewers of a programme is taken as the weight of the vertex. A set of programmes that are mutually exclusive in respect of time scheduling is called a session. We assume that a company sets the objective of selecting the popular programmes in k parallel sessions among different channels so as to make its commercial advertisement reach the maximum number of viewers, that is, a company selects k suitable programme slots simultaneously for advertisement. The aim of the paper is, therefore, to help the companies to select the programme slots, which are mutually exclusive with respect to the time schedule of telecasting time, in such a way that the total number of viewers of the selected programme in k parallel slots rises to the optimum level. It is shown that the solution of this problem is obtained by solving the maximum weight k-colouring problem on an interval graph. An algorithm is designed to solve this just-in-time optimization problem using O(kMn ² ) time, where n and M represent the total number of programmes of all channels and the upper bound of the viewers of all programmes of all channels respectively. The problem considered in this paper is a daily life problem which is modeled by k-colouring problem on interval graph. © 2016, Springer India Pvt. Ltd.

关键词： Design and analysis of algorithms Graph colouring Graph theory Interval graphs Modelling

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International Journal of applied and Computational mathematics 2021年第3期7卷 1-28页

作者： Sen, Sanjib Patra, Kartik Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 W.B. India Department of Mathematics Vivekananda Satavarshiki Mahavidyalaya Manikpara 721 513 W.B. India

In this present work, a new similarity measure of Gaussian fuzzy numbers has been proposed. The proposed method is based on the exponent distance about mean, standard deviation and height of the Gaussian fuzzy numbers. The similarity has been measured in two different forms of Gaussian fuzzy numbers. Some properties corresponding to the proposed new method of similarity measure have been discussed. Also, the proposed method has been demonstrated with some examples of Gaussian fuzzy numbers. Finally, the proposed similarity measure has been applied in a job selection procedure considering the linguistic values of the Gaussian fuzzy numbers. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Asymmetric form Gaussian fuzzy numbers Job selection Linguistic terms Linguistic values Similarity measure Symmetric form

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Pricing Policy with the Effect of Fairness Concern, Imprecise Greenness, and Prices in Imprecise Market for a Dual Channel

Pricing Policy with the Effect of Fairness Concern, Imprecis...

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International Conference on Nonlinear applied Analysis and Optimization, ICNAAO-2021

作者： Ganguly, Sanchari Das, Pritha Maiti, Manoranjan Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur WB Howrah711103 India Department of Applied Mathematics Oceanology and Computer Programming Vidyasagar University WB Midnapore721102 India

ISBN: (纸本)9789819905966

Fairness concern behavior, a well-known cognitive bias, refers to a person’s attitude of dissatisfaction for unequal pay-offs in someone’s favor. Against environmental pollution, many firms are focused on green manufacturing to maintain sustainable development. The adoption of online shopping by customers around the globe has altered the dynamics of competitiveness in the retail supply chain (SC). Considering the above facts, the effect of fairness concern on optimal prices and channel members’ profits in a two-level dual channel SC is investigated. Here, we consider an SC comprising a green manufacturer and a fair-minded retailer where the manufacturer produces and sells the green product through both offline and online channels to consumers. Due to uncertainty in the real world, the fuzziness is associated with market demand, price elasticity, and the coefficient of greenness. The fuzzy objectives and constraints are reduced to crisp ones using expectation and possibility measures, respectively. Both centralized and decentralized models (with and without cognitive bias) are formulated and solved by the Stackelberg game for the optimal prices and product greenness level. The models’ optimal solutions are analyzed and compared with the deterministic models numerically. The effects of the fairness concern coefficient on the optimal prices, product greenness level, and channel members’ profits are investigated. The sensitivity analyses are presented to study the effects of the fuzzy degree of customers’ sensitivity toward greenness on channel members’ profits. Retailer’s fairness is harmful to the manufacturer but beneficial for her own profit. Finally, some conclusions and managerial insights are presented. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Game theory

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Structural Design of Memristive Biosensors 8

Structural Design of Memristive Biosensors

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8th International Conference on Information, Control, and Communication Technologies, ICCT 2024

作者： Viktoriya, Zaripova Irina, Petrova Yuliya, Lezhnina Damir, Gimatdinov MIREA - Russian Technological University Department of Enterprise Programming Moscow Russia Astrakhan State Technical University Department of Higher and Applied Mathematics Astrakhan Russia

ISBN: (纸本)9798331517564

This paper considers importance of knowledge bases for the structural design of memristive biosensors, which offer innovative solutions in the field of biosensing due to their high sensitivity, fast response and low energy consumption. The paper analyzes modern approaches to the use of knowledge bases in the process of designing complex systems. The main stages of designing memristive biosensors are presented, at each of which the use of a knowledge base plays a key role. It's shown how knowledge bases help to systemize information, support decision making, improving design quality and speed up development. Examples of structural schemes and algorithms given in the article illustrate the practical application of representation models and knowledge extraction methods in engineering problems. The discussion includes a description of the creation and use of a knowledge base, the integration of interdisciplinary knowledge and the automation of design processes. The article emphasizes the relevance of the integration of knowledge bases and modern information technologies to improve the efficiency and reliability of the development of memristive biosensors, which makes it important for the scientific community and practitioners in the field of biosensors and engineering. © 2024 IEEE.

关键词： biomolecule detection biosensors fast response high sensitivity knowledge bases knowledge integration low power consumption memristors structural design

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Multi-choice stochastic bi-level programming problem in cooperative nature via fuzzy programming approach

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Journal of Industrial Engineering International 2016年第3期12卷 287-298页

作者： Maiti, Sumit Kumar Roy, Sankar Kumar School of Applied Sciences and Humanities Haldia Institute of Technology Purba Midnapore Haldia 721 157 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

In this paper, a Multi-Choice Stochastic Bi-Level programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general transformation technique with the help of binary variables is used to transform the multi-choice type cost coefficients of the objective functions of Decision Makers(DMs). Then the transformed problem is considered as a deterministic multi-choice bi-level programming problem. Finally, a numerical example is presented to illustrate the usefulness of the paper. © 2016, The Author(s).

关键词： Bi-level programming Fuzzy programming Multi-choice programming Non-linear programming Stochastic programming

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Some results on generalized interval-valued intuitionistic fuzzy sets

Some results on generalized interval-valued intuitionistic f...

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作者： Bhowmik, Monoranjan Pal, Madhumangal Department of Mathematics V.T.T. College Midnapore West Bengal-721101 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

In this paper, we define some results on generalized interval-valued intuitionistic fuzzy sets (GIVIFSs). In fact, all interval-valued intuitionistic fuzzy sets (IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. We define two composite relations, four types of reflexivity and irreflexivity of GIVIFSs with some of their properties. We define generalized interval-valued intuitionistic fuzzy relation (GIVIFR) with some results. Also we define two operators C and I with some properties over GIVIFSs. Finally, an illustrative example is given to using GIVIFSs in a decision making problem. © 2012 TFSA.

关键词： Decision making

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Modeling of Memory Dependent Derivative Under Three-Phase Lag in Generalized Thermo-Viscoelasticity

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International Journal of applied and Computational mathematics 2021年第6期7卷 1-20页

作者： Singh, Biswajit Sarkar, Smita Pal Barman, Krishnendu Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur Howrah 711103 West Bengal India Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Paschim Medinipur 721102 West Bengal India

In this study, a new generalized model of thermo-viscoelasticity with three phase-lag (TPL) theory concerning memory-dependent derivative (MDD) theory is emphasized. The governing combined equations of the novel model associated with kernel function and time delay are considered in a two-dimensional semi-infinite space. The bounding surface of the medium is assumed to be free of traction and subjected to time-dependent thermal loading. Using Laplace and Fourier Transform techniques, the problem is transformed from the space–time domain and then solved numerically. Suitable numerical technique is used to find the inversion of Fourier and Laplace transforms. In the simulation, the effects of the time-delay parameter and kernel function on the distributions of the displacement components, stresses and temperature field are studied and represented graphically. The results shows that the presence of TPL, the time-delay and kernel function extensively affect all the distributions. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Laplace and Fourier transform Memory dependent derivative Thermo-viscoelasticity Three phase-lag Vector matrix differential equation

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Dynamics of cholera outbreak with bacteriophage and periodic rate of contact

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International Journal of Dynamics and Control 2016年第3期4卷 284-292页

作者： Panja, Prabir Mondal, Shyamal Kumar Chattopadhyay, Joydev Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University MidnaporeW.B.721 102 India Agricultural and Ecological Research Unit ISI 203 B.T.Road Kolkata India

In this paper, a cholera epidemic model with periodic transmission rate has been considered and discussed. It is shown that the disease free equilibrium point is globally asymptotically stable and also seen that the cholera disease is disappeared if the basic reproduction number is less than one. When the basic reproduction number is grater than one, then the endemic equilibrium is globally asymptotically stable. Finally, numerical simulations have been given for the existence of the analytical results. © 2015, Springer-Verlag Berlin Heidelberg.

关键词： Bacteriophages

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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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A study on bipolar fuzzy planar graph and its application in image shrinking

A study on bipolar fuzzy planar graph and its application in...

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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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